Study guides, Class notes & Summaries

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-Power Rule Reverse the power rule for derivatives. d/dx (f*g) - ANSWER-fg' + gf' Product Rule What is the product rule in reverse? d/dx (f/g) Rule? - ANSWER-Quotient Rule When do you use t...

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 number (left) - ANSWER-and we say that "the limit of f(x) as x approaches c from the left 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 but less than c....

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^t) The constant P represents - ANSWER-y-intercept (Pb^t) The constant b represents - ANSWER-value of y is multiplied by b for every one unit increase of t b>1 - ANSWER-exponential growth b...

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 fraction - ANSWER-multiply top and bottom by common denominator of top fractions. Find instantaneous rate of change - ANSWER-use definition of derivative (difference quotient) as lim x-> 0 how...

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 integrals are inverses derivative of sin - ANSWER-cos derivative of cos - ANSWER--sin derivative of tan - ANSWER-sec^2 derivative of cot - ANSWER-csc^2 derivative of sec - ANSWER-secxtanx ...

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 - ANSWER-∑(-1)ⁿ(x²ⁿ)/(2n)!=1-x²/2!+x⁴/4!-x⁶/6!+... R=infinity Conditionally Convergent - ANSWER-A series is ∑ a_n is called conditionally convergent if it is convergent but not absolutely c...

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 function of t. At time t=1/2, what is the acceleration vector of the particle? - ANSWER-{12,4y"(1)} To what number does the series E (-e/pi)^k converge? - ANSWER-π/(π+e) Look at graph on ...

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 - ANSWER--sinx tan'x - ANSWER-sec^(2) x cot'x - ANSWER--csc^(2) x sec'x - ANSWER-(secx)(tanx) csc'x - ANSWER--(cscx)(cotx) arcsic'x - ANSWER-1/sq root(1-x^2) arccos'x - ANSWER-...

IVT (Intermediate Value Theorem) - answer-if f(x) is continuous on [a,b], there exists a point "c" between a and b such that f(a) ≤ c ≤ f(b) EVT (Extreme Value Theorem) - answer-if a function is

y = x^2 - answer- y^2 = x - answer- (x-h)^2 + (y-k)^2 = r^2 - answer- (x-h)^2/a^2 + (y-k)^2/b^2 = 1 - answer- (x-h)^2/a^2 - (y-k)^2/b^2 = 1 - answer-horizontal transverse axis (crosses x axis) (y-k)^2/a^2 - (x-h)^2/b^2 = 1 - answer-vertical transverse axis (crosses y axis) sphere equation - answer-(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2 a⋅b = ? - answer-|a||b|cosθ | axb | = ? - answer-|a||b|sinθ arc length of curve (L = ?) - answer- arc length function (s(t) = ?) - an...