- Study guides, Class notes & Summaries

What is a limit? - ANS A y-value that x approaches as you move along the graph Write: the limit as x approaches a of the function of x is equal to L - ANS lim(x→a) f(x)=L lim (x→-2) (x³+8)/(x+2)=? - ANS 12 T/F: The point doesn't have to exist for the limit to exist - ANS T What is a left sided limit? What is its notation? - ANS A limit that x approaches from the right side of the graph: lim(x→a⁻) f(x)=L What is a right sided limi...

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16 pages

Written in 2024/2025

Grade A+

DocLaura

AP Calculus BC Exam Review And Answers Formal definition of derivative - Answer- /.Alternate definition of derivative - Answer-limit as x approaches a of [f(x)-f(a)]/(x-a) /.When f '(x) is positive, f(x) is - Answer-increasing /.When f '(x) is negative, f(x) is - Answer-decreasing /.When f '(x) changes from negative to positive, f(x) has a - Answer-relative minimum /.When f '(x) changes from positive to negative, f(x) has a - Answer-relative maximum /.When f...

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6 pages

Written in 2024/2025

Grade A+

Brainariam

AP Calculus BC Exam Review Questions With Verified Answers Jump Discontinuity - Answer-When the two-sided limit doesn't exist because the one-sided limits aren't equal. /.Infinite Discontinuity - Answer-When the two-sided limit doesn't exist because it's unbounded. /.Removable Discontinuity - Answer-When the two-sided limit exists, but isn't equal to the function's value. /.Squeeze Theorem - Answer-ƒ(x) ≤ g(x) ≤ h(x) for all x and if the limit of ƒ(x) as x...

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6 pages

Written in 2024/2025

Grade A+

Brainariam

AP Calculus BC Exam Review Questions and Answers Average Rate of Change - Answer-Slope of secant line between two points, use to estimate instantanous rate of change at a point. /.Instantenous Rate of Change - Answer-Slope of tangent line at a point, value of derivative at a point /.Definition of Derivative - Answer-limit as h approaches 0 of [f(a+h)-f(a)]/h or limit as x approaches a of [f(x)-f(a)]/(x-a) /.When f '(x) is positive, f(x) is - Answer-increasing /.When f '(x)...

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21 pages

Written in 2024/2025

Grade A+

Brainariam

AP Calculus BC Final Exam Questions and Answers taking a continuous object and breaking it up to approximate (advantages, disadvantages) - Answer-disadvantage- more pieces to deal with advantage- more accurate estimate /.Calculus - Answer-all about limits and the attempt of closing in on an exact value of an answer by using finer and finer approximations /.limit - Answer-o the idea of a limit is that we are attempting to see what the output (y) approaches, if anything, as the input (x...

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7 pages

Written in 2024/2025

Grade A+

Brainariam

AP Calculus BC Study Guide Exam Questions And Answers Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm? Which of the following represents the notation of our final answer to this problem? - Answer-dA/dt = 40pi cm²/min /.Which of the following are acceptable guidelines for solving Related Rates problems? - Answer--Label all quantities that can change as variable...

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44 pages

Written in 2024/2025

Grade A+

Brainariam

AP Calculus BC Study Guide with complete solutions sin² θ + cos² θ = - Answer-1 /.1 + tan² θ = - Answer-sec² θ /.1 + cot² θ = - Answer-csc² θ /.sin(-θ) = - Answer--sin θ /.cos(-θ) = - Answer-cos θ /.tan(-θ) = - Answer--tan θ /.sin(A + B) = - Answer-sinAcosB + sinBcosA /.sin(A - B) = - Answer-sinAcosB - sinBcosA /.cos(A + B) = - Answer-cosAcosB - sinAsinB /.cos(A - B) = - Answer-cosAcosB + sinAsinB /.sin 2θ = - Answer-2sinθcosθ /.cos 2θ = ...

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10 pages

Written in 2024/2025

Grade A+

Brainariam

Tangent Line - ANSWERStraight line on the curve at a given point that can be used to estimate values near by Slope - ANSWERRise over run Speeding Up - ANSWERAcceleration has the same sign as Velocity Slowing Down - ANSWERAcceleration has the opposite sign as Velocity Area Under the Curve - ANSWERIntegral or antiderivative Area Between Curves - ANSWERwith f(x) on top and g(x) on bottom a and b represent bounds or where the two graphs intersect Instantaneous Rate of Change - A...

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3 pages

Written in 2024/2025

Grade A+

papersbyjol

Intermediate Value Theorem - ANSWERIf f(x) is continuous on closed interval [a,b] and f(a) is not equal to f(b), then for every value M between f(a) and f(b), there exists at least 1 value c within (a,b) such that f(c) = M Average Rate of Change - ANSWERSlope of secant line between two points, use to estimate instantanous rate of change at a point. Instantenous Rate of Change - ANSWERSlope of tangent line at a point, value of derivative at a point Formal definition of derivative - ANSWE...

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8 pages

Written in 2024/2025

Grade A+

papersbyjol

AP Calculus BC Exam Questions With All Correct Answers Formal definition of derivative - Answer- /.Alternate definition of derivative - Answer-limit as x approaches a of [f(x)-f(a)]/(x-a) /.When f '(x) is positive, f(x) is - Answer-increasing /.When f '(x) is negative, f(x) is - Answer-decreasing /.When f '(x) changes from negative to positive, f(x) has a - Answer-relative minimum /.When f '(x) changes from positive to negative, f(x) has a - Answer-relative maximu...

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6 pages

Written in 2024/2025

Grade A+

Brainariam

given absolute value in formula: what should you do? - ANSWERwrite out separate parts; test +/- using number line method; write out as a *piecewise* the upper or lower half of a parabola [ex: x = √(y)] - ANSWERthe lower half is usually the negative part of ±, and vise versa when changing/altering a function, how does the domain change? - ANSWERthe domain is restricted to the original domain if a function is one-to-one, or x is in the range of f/the domain of f⁻¹ - ANSWERƒ(ƒ⁻¹...

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4 pages

Written in 2024/2025

Grade A+

papersbyjol

Product rule Derivatives - ANSWER Volume of Disc - ANSWER Integral of tan x - ANSWER Integral of cot x - ANSWER Integral of sec x tan x - ANSWER Integral of csc^2 x - ANSWER Integral of csc x cot x - ANSWER Volume of Washer - ANSWER Volume of Shell - ANSWER Volume of Cross Section - ANSWER Second Fundamental Theorem - ANSWER Area of Trapezoid - ANSWER Trapezoidal Rul

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3 pages

Written in 2024/2025

Grade A

papersbyjol

Intermediate Value Theorem - ANSWERIf f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. Formal definition of derivative - ANSWER Alternate definition of derivative - ANSWERlimit as x approaches a of [f(x)-f(a)]/(x-a) When f '(x) is positive, f(x) is - ANSWERincreasing Average Rate of Change - ANSWERSlope of secant line between two points, use to estimate instantanous rate of change at a point. Instantenous Rate of Change - ANSWERSlop...

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3 pages

Written in 2024/2025

Grade A+

papersbyjol

taking a continuous object and breaking it up to approximate (advantages, disadvantages) - ANSWERdisadvantage- more pieces to deal with advantage- more accurate estimate Calculus - ANSWERall about limits and the attempt of closing in on an exact value of an answer by using finer and finer approximations limit - ANSWERthe idea of a limit is that we are attempting to see what the output (y) approaches, if anything, as the input (x) approaches a particular value limit (L) can be one of fo...

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7 pages

Written in 2024/2025

Grade A

papersbyjol

Average Rate of Change - ANSWERSlope of secant line between two points, use to estimate instantanous rate of change at a point. Instantenous Rate of Change - ANSWERSlope of tangent line at a point, value of derivative at a point Definition of Derivative - ANSWERlimit as h approaches 0 of [f(a+h)-f(a)]/h or limit as x approaches a of [f(x)-f(a)]/(x-a) When f '(x) is positive, f(x) is - ANSWERincreasing When f '(x) is negative, f(x) is - ANSWERdecreasing When f '(x) changes...

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19 pages

Written in 2024/2025

Grade A+

papersbyjol

Jump Discontinuity - ANSWERWhen the two-sided limit doesn't exist because the one-sided limits aren't equal. Infinite Discontinuity - ANSWERWhen the two-sided limit doesn't exist because it's unbounded. Removable Discontinuity - ANSWERWhen the two-sided limit exists, but isn't equal to the function's value. Squeeze Theorem - ANSWERƒ(x) ≤ g(x) ≤ h(x) for all x and if the limit of ƒ(x) as x→c = L and the limit of h(x) as x→c = L, then the limit of g(x) as x→c...

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5 pages

Written in 2024/2025

Grade A+

papersbyjol

sin² θ + cos² θ = - ANSWER1 1 + tan² θ = - ANSWERsec² θ 1 + cot² θ = - ANSWERcsc² θ sin(-θ) = - ANSWER-sin θ cos(-θ) = - ANSWERcos θ tan(-θ) = - ANSWER-tan θ sin(A + B) = - ANSWERsinAcosB + sinBcosA sin(A - B) = - ANSWERsinAcosB - sinBcosA cos(A + B) = - ANSWERcosAcosB - sinAsinB cos(A - B) = - ANSWERcosAcosB + sinAsinB sin 2θ = - ANSWER2sinθcosθ cos 2θ = - ANSWERcos² θ - sin² θ = 2cos² θ - 1 = 1 - 2sin² θ tan θ = - ANSWERsin...

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10 pages

Written in 2024/2025

Grade A+

papersbyjol

Squeeze Theorem - ANSWERIf h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim x→c ƒ(x) exists and equals L. Continuity - ANSWERA function ƒ is continuous at c if: a. ƒ(c) is defined b. lim x→c ƒ(x) exists c. lim x→c ƒ(x) = ƒ(c) Intermediate Value Theorem - ANSWERIf ƒ is continuous on an interval [a,b] and k is any number between ƒ(a) and ƒ(b), there is at least one number c in ...

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4 pages

Written in 2024/2025

Grade A+

papersbyjol

Calc BC exam questions and answers

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6 pages

Written in 2024/2025

Grade A+

millyphilip

AP Calculus BC Unit 12 Exam Questions and Answers

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2 pages

Written in 2024/2025

Grade A+

millyphilip