Exam (elaborations) AP Calc AB Exam Must Knows Exam Questions with Correct Answers Exam (elaborations) AP Calculus AB Exam Review Questions and Answers Exam (elaborations) AP Calculus AB Final Multiple Choice Exam Questions with Complete Solutions Exam (elaborations) AP Calculus AB Study Gui...
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d/dx [e^x] - ANSWER-e^x d/dx [-2/3 e^(-1/2x)] - ANSWER--2/3 e^(-1/2x) * (-1/2) (lim as h approaches 0) [(f(x+h)-f(x))/h] - ANSWER-Msec (average velocity) If differentiable - ANSWER-it's continuous. If continuous - ANSWER-not necessarily differentiable. sin'x - ANSWER-cosx cos'x ...
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Add to cartd/dx [e^x] - ANSWER-e^x d/dx [-2/3 e^(-1/2x)] - ANSWER--2/3 e^(-1/2x) * (-1/2) (lim as h approaches 0) [(f(x+h)-f(x))/h] - ANSWER-Msec (average velocity) If differentiable - ANSWER-it's continuous. If continuous - ANSWER-not necessarily differentiable. sin'x - ANSWER-cosx cos'x ...
If f(x)=cos^2(3x-5) f'(x)= - ANSWER--6sin(3x-5)cos(3x-5) ∫1/t√t dt= - ANSWER--2t^(-1/2) + c If f(x)= (5-x)/(x^3+2) f'(x)= - ANSWER-(2x^3-15x^2-2)/(x^3+2)^2 The position of a particle moving in the xy-plane is given by the vector {4t^3,y(2t)}, where y is a twice-differeniable fun...
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Add to cartIf f(x)=cos^2(3x-5) f'(x)= - ANSWER--6sin(3x-5)cos(3x-5) ∫1/t√t dt= - ANSWER--2t^(-1/2) + c If f(x)= (5-x)/(x^3+2) f'(x)= - ANSWER-(2x^3-15x^2-2)/(x^3+2)^2 The position of a particle moving in the xy-plane is given by the vector {4t^3,y(2t)}, where y is a twice-differeniable fun...
McLaurin Series for 1/(1-x) - ANSWER-∑xⁿ=1+x+x²+x³+x⁴+... R=1 McLaurin Series for e^x - ANSWER-∑xⁿ/n!=1+x/1!+x²/2!+x³/3!+... R=infinity McLaurin Series for sinx - ANSWER-∑(-1)ⁿ(x²ⁿ⁺¹)/(2n+1)!=x-x³/3!+x⁵/5!-x⁷/7!+... R=infinity McLaurin Series for cosx - ANSWE...
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Add to cartMcLaurin Series for 1/(1-x) - ANSWER-∑xⁿ=1+x+x²+x³+x⁴+... R=1 McLaurin Series for e^x - ANSWER-∑xⁿ/n!=1+x/1!+x²/2!+x³/3!+... R=infinity McLaurin Series for sinx - ANSWER-∑(-1)ⁿ(x²ⁿ⁺¹)/(2n+1)!=x-x³/3!+x⁵/5!-x⁷/7!+... R=infinity McLaurin Series for cosx - ANSWE...
A function is continuous at x=A when... - ANSWER-1.) f(A) exists 2.) The limit exists -the LHL and RHL are equal 3.) f(A)=limit Limit definition of the derivative - ANSWER-the limit as h approaches zero is [f(x+h)-f(x)]/h Fundamental Theorem of Calculus I - ANSWER-Derivatives and integr...
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Add to cartA function is continuous at x=A when... - ANSWER-1.) f(A) exists 2.) The limit exists -the LHL and RHL are equal 3.) f(A)=limit Limit definition of the derivative - ANSWER-the limit as h approaches zero is [f(x+h)-f(x)]/h Fundamental Theorem of Calculus I - ANSWER-Derivatives and integr...
Find the average rate of change of f(x) on [a,b] - ANSWER-find: [f(b)- f(a)]/ (b-a) Difference Quotient - ANSWER-f(x+h)-f(x)/h, where h does not equal 0. using difference quotient when f(x) is a radical - ANSWER-multiply top and bottom by conjugate using difference quotient when f(x) is a f...
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Add to cartFind the average rate of change of f(x) on [a,b] - ANSWER-find: [f(b)- f(a)]/ (b-a) Difference Quotient - ANSWER-f(x+h)-f(x)/h, where h does not equal 0. using difference quotient when f(x) is a radical - ANSWER-multiply top and bottom by conjugate using difference quotient when f(x) is a f...
Linear Function - ANSWER-F(x)=mx+b Quadratic Function - ANSWER-F(x)=ax^2+bx+c Exponential Function - ANSWER-F(x)=ab^x Logarithmic Function - ANSWER-F(x)=Logbx=y or b^y=x Finding the slope of a line - ANSWER-y-y^1=m(x-x^1) Exponential Function in General Form - ANSWER-A(t)=Pb^t (Pb^...
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Add to cartLinear Function - ANSWER-F(x)=mx+b Quadratic Function - ANSWER-F(x)=ax^2+bx+c Exponential Function - ANSWER-F(x)=ab^x Logarithmic Function - ANSWER-F(x)=Logbx=y or b^y=x Finding the slope of a line - ANSWER-y-y^1=m(x-x^1) Exponential Function in General Form - ANSWER-A(t)=Pb^t (Pb^...
definition of a finite limit at a real number - ANSWER-and we say that "the limit of f(x) as x approaches c* is L" if we can make the values of f(x) as close to L as we want by taking x close enough to c on either side of c but not equal to c. definition of finite one-sided limits at a real num...
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Add to cartdefinition of a finite limit at a real number - ANSWER-and we say that "the limit of f(x) as x approaches c* is L" if we can make the values of f(x) as close to L as we want by taking x close enough to c on either side of c but not equal to c. definition of finite one-sided limits at a real num...
sin²x + cos² x=? - ANSWER-1 Which Pythagorean formula = 1? 1 + tan² x=? - ANSWER-sec²(x) Which Pythagorean formula = sec²(x)? 1 + cot² x=? - ANSWER-csc² x Which Pythagorean formula = csc² x sin(-x)=? - ANSWER--sin x -sin(x) = sin(-x) or only -sin(x)? d/dx (x^n) Rule? - ANSWER...
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Add to cartsin²x + cos² x=? - ANSWER-1 Which Pythagorean formula = 1? 1 + tan² x=? - ANSWER-sec²(x) Which Pythagorean formula = sec²(x)? 1 + cot² x=? - ANSWER-csc² x Which Pythagorean formula = csc² x sin(-x)=? - ANSWER--sin x -sin(x) = sin(-x) or only -sin(x)? d/dx (x^n) Rule? - ANSWER...
Constant Rule - ANSWER-d/dx [c] = 0 Constant Multiple Rule - ANSWER-d/dx [cf(x)]=cf'(x) Sum Rule - ANSWER-d/dx [f(x)+g(x)] = f'(x)+g'(x) Difference Rule - ANSWER-d/dx [f(x)-g(x)] = f'(x)-g'(x) Product Rule - ANSWER-d/dx [f(x)*g(x)] = f(x)g'(x) + f'(x)g(x) Quotient Rule - ANSWER...
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Add to cartConstant Rule - ANSWER-d/dx [c] = 0 Constant Multiple Rule - ANSWER-d/dx [cf(x)]=cf'(x) Sum Rule - ANSWER-d/dx [f(x)+g(x)] = f'(x)+g'(x) Difference Rule - ANSWER-d/dx [f(x)-g(x)] = f'(x)-g'(x) Product Rule - ANSWER-d/dx [f(x)*g(x)] = f(x)g'(x) + f'(x)g(x) Quotient Rule - ANSWER...
What can be used to determine whether a relation satisfies the definition of a function? - ANSWER-Vertical Line Test What are the four ways a function can be represented? - ANSWER-numerically, algebraically, verbally, graphically What must be met in order to be considered a function (basic lev...
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Add to cartWhat can be used to determine whether a relation satisfies the definition of a function? - ANSWER-Vertical Line Test What are the four ways a function can be represented? - ANSWER-numerically, algebraically, verbally, graphically What must be met in order to be considered a function (basic lev...
Average Rate of Change - ANSWER-Slope of two points Instantaneous Rate of Change - ANSWER-Derivative Derivative is - ANSWER-the slope of the tangent line at one point Mean Value Theorem - ANSWER-If a function is both continuous and differentiable on an interval, then there exists some 'c'...
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Add to cartAverage Rate of Change - ANSWER-Slope of two points Instantaneous Rate of Change - ANSWER-Derivative Derivative is - ANSWER-the slope of the tangent line at one point Mean Value Theorem - ANSWER-If a function is both continuous and differentiable on an interval, then there exists some 'c'...
What is the difference quotient? - ANSWER-f(x+h)-(f(x) _______________ h Lim f(x) = 4 x > 2 - ANSWER-As x approaches 2, y is very close to 4 Lim f(x) = 2 x > 2 - ANSWER-As x approaches 2, y is either undef. or = to 4 Does the limit exist? Lim f(x) = 4 x > 2 - ANSWER- Li...
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Add to cartWhat is the difference quotient? - ANSWER-f(x+h)-(f(x) _______________ h Lim f(x) = 4 x > 2 - ANSWER-As x approaches 2, y is very close to 4 Lim f(x) = 2 x > 2 - ANSWER-As x approaches 2, y is either undef. or = to 4 Does the limit exist? Lim f(x) = 4 x > 2 - ANSWER- Li...
Power Rule - ANSWER-Example: y=x^67, y'=67x^66 Constant Multiple Rule - ANSWER-Examples: y=7x^8, y'=7(8)x^7 Sum Rule - ANSWER- IF y=e^x then y'=e^x - ANSWER-IF y=e^x then y'=e^x Product rule - ANSWER-_____ x ______ + ______ x ______ Quotient Rule - ANSWER-HoDiHi - HiDiHo/ Ho^2 ...
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Add to cartPower Rule - ANSWER-Example: y=x^67, y'=67x^66 Constant Multiple Rule - ANSWER-Examples: y=7x^8, y'=7(8)x^7 Sum Rule - ANSWER- IF y=e^x then y'=e^x - ANSWER-IF y=e^x then y'=e^x Product rule - ANSWER-_____ x ______ + ______ x ______ Quotient Rule - ANSWER-HoDiHi - HiDiHo/ Ho^2 ...
True or False: f(x)= (1/3)x^3 - x^2 - 3x +1 has two critical numbers - ANSWER-False x= -1 Find the number of critical numbers for f(x)= (cosx)^2- sinx on [0, 2pi] - ANSWER-4 critical numbers: x= pi/2, 7pi/6, 3pi/2, 11pi/6 Find the absolute maximum value of f(x)= sinx on [-pi/3, pi/4] - ANSW...
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Add to cartTrue or False: f(x)= (1/3)x^3 - x^2 - 3x +1 has two critical numbers - ANSWER-False x= -1 Find the number of critical numbers for f(x)= (cosx)^2- sinx on [0, 2pi] - ANSWER-4 critical numbers: x= pi/2, 7pi/6, 3pi/2, 11pi/6 Find the absolute maximum value of f(x)= sinx on [-pi/3, pi/4] - ANSW...
Section 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of chan...
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Add to cartSection 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of chan...
evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a ...
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Add to cartevaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a ...
Section 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of chan...
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Add to cartSection 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of chan...
evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a ...
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Add to cartevaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a ...
Vertical Asymptote - ANSWER-Set Denominator equal to zero Horizontal asymptote - ANSWER-set numerator equal to zero Rolles theorem states there is... - ANSWER-a tangent line at some point on a closed interval [a,b] if the following hold true a) continuous b) differentiable c) f(a)=f(b) I...
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Add to cartVertical Asymptote - ANSWER-Set Denominator equal to zero Horizontal asymptote - ANSWER-set numerator equal to zero Rolles theorem states there is... - ANSWER-a tangent line at some point on a closed interval [a,b] if the following hold true a) continuous b) differentiable c) f(a)=f(b) I...
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INTG(sin(x) dx) - ANSWER--cos(x) + C INTG(cos(x) dx) - ANSWER-sin(x) + C INTG((sec(x))^2 dx) - ANSWER-tan(x) + C INTG((csc(x))^2 dx) - ANSWER--cot(x) + C INTG(sec(x)*tan(x) dx) - ANSWER-sec(x) + C INTG(csc(x)*cot(x) dx) - ANSWER--csc(x) + C INTG(b^x dx) - ANSWER-(1/ln(b))*b^x + C ...
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Add to cartINTG(sin(x) dx) - ANSWER--cos(x) + C INTG(cos(x) dx) - ANSWER-sin(x) + C INTG((sec(x))^2 dx) - ANSWER-tan(x) + C INTG((csc(x))^2 dx) - ANSWER--cot(x) + C INTG(sec(x)*tan(x) dx) - ANSWER-sec(x) + C INTG(csc(x)*cot(x) dx) - ANSWER--csc(x) + C INTG(b^x dx) - ANSWER-(1/ln(b))*b^x + C ...
volume equation - ANSWER-v=4/3 r^3 related rate problems - ANSWER-treat all variables as functions of time, use implicit differentiation to produce equalities which can be solved for the desired rates linear approximation equation - ANSWER-f'(a)(x-a)+f(a) linear approximation - ANSWER-appr...
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Add to cartvolume equation - ANSWER-v=4/3 r^3 related rate problems - ANSWER-treat all variables as functions of time, use implicit differentiation to produce equalities which can be solved for the desired rates linear approximation equation - ANSWER-f'(a)(x-a)+f(a) linear approximation - ANSWER-appr...
Power Rule - ANSWER-d/dx x^n = nx^n-1 d/dx [c] - ANSWER-0 d/dx [sinx] - ANSWER-cosx d/dx [cosx] - ANSWER--sinx d/dx [e^x] - ANSWER-e^x Product Rule - ANSWER-d/dx [f(x) g(x)] = f'g+g'f Quotient Rule - ANSWER-d/dx [f(x)/g(x)] = f'g-g'f/g^2 d/dx [tanx] - ANSWER-sec^2x d/dx [...
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Add to cartPower Rule - ANSWER-d/dx x^n = nx^n-1 d/dx [c] - ANSWER-0 d/dx [sinx] - ANSWER-cosx d/dx [cosx] - ANSWER--sinx d/dx [e^x] - ANSWER-e^x Product Rule - ANSWER-d/dx [f(x) g(x)] = f'g+g'f Quotient Rule - ANSWER-d/dx [f(x)/g(x)] = f'g-g'f/g^2 d/dx [tanx] - ANSWER-sec^2x d/dx [...
What will calculus enable you to do? - ANSWER-Find the volumes of oddly shaped objects Consider the function y=x^2-2x+1. What is the slope of the tangent line at x=2? - ANSWER-2 What is the average rate of change of the function y=2x^2+3 between x=x1 and x=x2 - ANSWER-2(x2+X1) What is the s...
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Add to cartWhat will calculus enable you to do? - ANSWER-Find the volumes of oddly shaped objects Consider the function y=x^2-2x+1. What is the slope of the tangent line at x=2? - ANSWER-2 What is the average rate of change of the function y=2x^2+3 between x=x1 and x=x2 - ANSWER-2(x2+X1) What is the s...
definition of a limit - ANSWER-A limit is a number that a function approaches as x approaches a value Limit equation - ANSWER-f(x+h)-f(x)/h e ln(x) - ANSWER-x e^x e^y - ANSWER-e^(x+y) e^xy - ANSWER-(e^x)^y lne^x - ANSWER-x ln(xy) - ANSWER-ln(x)+ln(y) ln(x^y ) - ANSWER-ylnx ta...
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Add to cartdefinition of a limit - ANSWER-A limit is a number that a function approaches as x approaches a value Limit equation - ANSWER-f(x+h)-f(x)/h e ln(x) - ANSWER-x e^x e^y - ANSWER-e^(x+y) e^xy - ANSWER-(e^x)^y lne^x - ANSWER-x ln(xy) - ANSWER-ln(x)+ln(y) ln(x^y ) - ANSWER-ylnx ta...
Points of Inflection - ANSWER-If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f" is undefined at c Critical Value - ANSWER-Where first derivative is 0 or undefined Find absolute extrema - ANSWER-Use critical values and END POINTS in the function Horizontal ...
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Add to cartPoints of Inflection - ANSWER-If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f" is undefined at c Critical Value - ANSWER-Where first derivative is 0 or undefined Find absolute extrema - ANSWER-Use critical values and END POINTS in the function Horizontal ...
equation of a tangent line - ANSWER-y= f'(x)(x-x1)+f(x) difference quotient/ average rate of change (AROC) - ANSWER-f(x+h)-f(x)/h point slope form of a line - ANSWER-y-y1=m(x-x1) derivative is the same as... - ANSWER--slope of the tangent line -instantaneous rate of change -marginal (cos...
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Add to cartequation of a tangent line - ANSWER-y= f'(x)(x-x1)+f(x) difference quotient/ average rate of change (AROC) - ANSWER-f(x+h)-f(x)/h point slope form of a line - ANSWER-y-y1=m(x-x1) derivative is the same as... - ANSWER--slope of the tangent line -instantaneous rate of change -marginal (cos...
power rule - ANSWER-if y = x^k -- then, k * x^k⁻¹ product rule - ANSWER-f(x) • g(x) then [f(x)•g(x)' + f(x)'•g(x)] quotient rule - ANSWER-D(x) • N'(x) - N(x) •D'(x) --------------------- [D(x)]² extended power rule - ANSWER-[g(x)]^k = k[g(x)]^k-1 • g(x)' chain...
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Add to cartpower rule - ANSWER-if y = x^k -- then, k * x^k⁻¹ product rule - ANSWER-f(x) • g(x) then [f(x)•g(x)' + f(x)'•g(x)] quotient rule - ANSWER-D(x) • N'(x) - N(x) •D'(x) --------------------- [D(x)]² extended power rule - ANSWER-[g(x)]^k = k[g(x)]^k-1 • g(x)' chain...
Read the following three statements A, B and C. Based on the statements A, B and C, given above, which one of the following is correct? - ANSWER-C. If f'(x) > 0 in (a,b) and f"(x) < 0 in (a,b), then the graph of f(x) is decreasing AND concave down in (a,b). C. The Statements A and B ...
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Add to cartRead the following three statements A, B and C. Based on the statements A, B and C, given above, which one of the following is correct? - ANSWER-C. If f'(x) > 0 in (a,b) and f"(x) < 0 in (a,b), then the graph of f(x) is decreasing AND concave down in (a,b). C. The Statements A and B ...
what does a function have to be in order for it to have a constant rate of change - ANSWER-linear what is slope intercept form - ANSWER-y=mx+b whats the equation of a line - ANSWER-y-y initial=m(x-x initial) in a problem showing attendance at NFL games over the years, what will the average ...
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Add to cartwhat does a function have to be in order for it to have a constant rate of change - ANSWER-linear what is slope intercept form - ANSWER-y=mx+b whats the equation of a line - ANSWER-y-y initial=m(x-x initial) in a problem showing attendance at NFL games over the years, what will the average ...
Let g(x)=x^4+4x^3. How many relative extrema does g have? - ANSWER-B. One An object moves along a straight line so that at any time t its acceleration is given by a(t)=6t. At time t=0, the objects velocity is 10 and the position is 7. What is the object's position at t=2? - ANSWER-D. 35 Let g...
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Add to cartLet g(x)=x^4+4x^3. How many relative extrema does g have? - ANSWER-B. One An object moves along a straight line so that at any time t its acceleration is given by a(t)=6t. At time t=0, the objects velocity is 10 and the position is 7. What is the object's position at t=2? - ANSWER-D. 35 Let g...
Find the limit as x approaches a number. - ANSWER-Plug in the number. If you get 0/0, factor and cancel then plug in again. Find the limit as x approaches infinity. - ANSWER-Degree on top greater -> DNE Degree on bottom greater -> zero Degrees the same -> ratio of leading coefficients ...
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Add to cartFind the limit as x approaches a number. - ANSWER-Plug in the number. If you get 0/0, factor and cancel then plug in again. Find the limit as x approaches infinity. - ANSWER-Degree on top greater -> DNE Degree on bottom greater -> zero Degrees the same -> ratio of leading coefficients ...
Integral of cosx - ANSWER-sinx+c Integral of sin x - ANSWER--cosx+c Integral of sec^2x - ANSWER-tanx+c Integral of secxtanx - ANSWER-secx+c Integral of csc^2x - ANSWER--cotx+c Integral of cscxcotx - ANSWER--cscx+c If a trapezoidal sum overapproximates ∫0 to 4 f(x)dx, and a right ...
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Add to cartIntegral of cosx - ANSWER-sinx+c Integral of sin x - ANSWER--cosx+c Integral of sec^2x - ANSWER-tanx+c Integral of secxtanx - ANSWER-secx+c Integral of csc^2x - ANSWER--cotx+c Integral of cscxcotx - ANSWER--cscx+c If a trapezoidal sum overapproximates ∫0 to 4 f(x)dx, and a right ...
The slope of a secant line represents what kind of change? - ANSWER-Average roc The slope of a tangent line represents what kind of change? - ANSWER-Instantaneous roc What kind of change does an integral represent? - ANSWER-Total change Explain what a derivative is graphically. - ANSWER-Slo...
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Add to cartThe slope of a secant line represents what kind of change? - ANSWER-Average roc The slope of a tangent line represents what kind of change? - ANSWER-Instantaneous roc What kind of change does an integral represent? - ANSWER-Total change Explain what a derivative is graphically. - ANSWER-Slo...
Derivative of sin(x) - ANSWER-cos(x) Derivative of cos(x) - ANSWER--sin(x) Derivative of tan(x) - ANSWER-sec^2(x) Derivative of sec(x) - ANSWER-sec(x) tan(x) Derivative of cot(x) - ANSWER--csc^2(x) Derivative of csc(x) - ANSWER--csc(x) cot(x) Limits of infinity with highest exponen...
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Add to cartDerivative of sin(x) - ANSWER-cos(x) Derivative of cos(x) - ANSWER--sin(x) Derivative of tan(x) - ANSWER-sec^2(x) Derivative of sec(x) - ANSWER-sec(x) tan(x) Derivative of cot(x) - ANSWER--csc^2(x) Derivative of csc(x) - ANSWER--csc(x) cot(x) Limits of infinity with highest exponen...
Find all points of relative minima and maxima: y = x^2 + 6x + 5 - ANSWER-minima at (-3, -4) Find all points of relative minima and maxima: y = -12/(x^2 + 3) - ANSWER-minima at (0, -4) Find the open intervals where the function is concave up and concave down. y = (2x-12)^(1/3) - ANSWE...
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Add to cartFind all points of relative minima and maxima: y = x^2 + 6x + 5 - ANSWER-minima at (-3, -4) Find all points of relative minima and maxima: y = -12/(x^2 + 3) - ANSWER-minima at (0, -4) Find the open intervals where the function is concave up and concave down. y = (2x-12)^(1/3) - ANSWE...
d sin x - ANSWER-cos x d cos x - ANSWER-- sin x d tan x - ANSWER-sec^2 x ∫sin x - ANSWER-- cos x ∫cos x - ANSWER-sin x ∫ sec^2 x - ANSWER-tan x d ln U - ANSWER-dU / U ∫ e^U dU - ANSWER-e^U ∫ dU / U - ANSWER-ln |U| e^ln x - ANSWER-x ln e^x - ANSWER-x ln e - ...
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Add to cartd sin x - ANSWER-cos x d cos x - ANSWER-- sin x d tan x - ANSWER-sec^2 x ∫sin x - ANSWER-- cos x ∫cos x - ANSWER-sin x ∫ sec^2 x - ANSWER-tan x d ln U - ANSWER-dU / U ∫ e^U dU - ANSWER-e^U ∫ dU / U - ANSWER-ln |U| e^ln x - ANSWER-x ln e^x - ANSWER-x ln e - ...
Derivative of arcsin(x) - ANSWER-1/sqrt(1-x^2) Derivative of arccos(x) - ANSWER--1/sqrt(1-x^2) derivative of arctan(x) - ANSWER-1/(1+x^2) derivative of arccsc(x) - ANSWER--1/(|x|√(x²-1)) derivative of arcsec(x) - ANSWER-1/(abs(x)sqrt(x^2-1)) derivative of arccot(x) - ANSWER--1/(1+x...
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Add to cartDerivative of arcsin(x) - ANSWER-1/sqrt(1-x^2) Derivative of arccos(x) - ANSWER--1/sqrt(1-x^2) derivative of arctan(x) - ANSWER-1/(1+x^2) derivative of arccsc(x) - ANSWER--1/(|x|√(x²-1)) derivative of arcsec(x) - ANSWER-1/(abs(x)sqrt(x^2-1)) derivative of arccot(x) - ANSWER--1/(1+x...
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