# Differentiation Questions and Answers

Calculus

Differentiation27 3 J 2 30 A m 3 n B m 2 5 n 3 C m n 2 3 D m 3 n 2 28 4 5 3 45 y 5 3 3 S 6 A x B x C 5 6 D x S 6 6 5 3 y 39 6 5 6 3 y y 5 y 5

Calculus

DifferentiationConsider the curve given by the parametric equations a Determine the point on the curve where the tangent is horizontal t x t t 147 y 2 t 147 b Determine the points t t2 where the tangent is vertical and t t t

Calculus

DifferentiationQuestion Evaluate the indefinite integral given below Provide your answer below X5 x 2 dx

Calculus

DifferentiationEvaluate the indefinite integral given below using the indicated substitution 3 4 42 x 3a 2 da U 3x x Provide your answer below

Calculus

DifferentiationEvaluate the indefinite integral given below using the indicated substitution fa Provide your answer below 17 8x dx u 17 8x

Calculus

DifferentiationFind the area of the triangle having the indicated angle and sides Round your a B 125 a 94 c 39

Calculus

DifferentiationUse the Law of Sines to solve the triangle Let a 12 mm Round your answers for b and c to two decimal places O b mm mm b 350 C 55 a B

Calculus

DifferentiationSolve the logarithmic equation Round your answer to three decimal places log10 x 1133 X 1

Calculus

DifferentiationFind the inverse function of f informally Verify that f f 1 x x and f f x f x 8 x 2 f 1 x X

Calculus

DifferentiationFind the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative F x 2 t t t

Calculus

DifferentiationOrphof 9 Let be the function defined by f x cos 2x Leth be the function whose graph consisting of five line segments is shown in the figure above a Find the slope of the line tangent to the graph off at x H b Let k be the function defined by k x h f x Find k x

Calculus

DifferentiationExample 8 Is the function given by f x x 1 for x 4 x 7 for x 4 continuous at x 4 Why or why not

Calculus

Differentiation7 Patrick was asked to write an expression equivalent to 2log3x w5 He came up with 6log3x 5log3w Determine if his expression is equivalent or not Explain your answer

Calculus

DifferentiationUse the Laws of Logarithms to expand the expression log V 7x y 1 1 9 log 7 x log 7 y

Calculus

DifferentiationThe bounded area between the curves f x 15x4 and g x 15x is Your answer should be a number

Calculus

DifferentiationFind the area of the triangle determined by the points P Q R P 1 1 2 Q 2 0 1 R 0 2 1

Calculus

DifferentiationQuestion 1 Solve the given inequality Enter your answer using interval notation and exact values 2x 724x 3

Calculus

DifferentiationNext question Identify the domain of the following functions a f x log 4x 7 00 17 4 Domain b f x ln 3x 2 Domain Get a similar question c f x log 2x 8 Domain Question Help Message instructor OF You ca

Calculus

Differentiationa Calculate the definite integral f x dx by referring to the figure on the right with the indicated areas a b Ay Area A 1 204 Area B 2 308 Area C 3 079 Area D 1 687

Calculus

DifferentiationThe graph of y f x solid and its tangent line at x 0 dashed is shown a second point on the tangent line is also marked Assume f x is continuous 10 9 8 7 6 5 Find f x lim x 0 x f x lim 204e 4 10 9 8 9 1 1 5 6 8 9 10

Calculus

Differentiationt x 9y x 2 7y y 1 0 0 5 0 5 C 4 6 8 0 1 0 F 1 0 0 5 R 8 89 0 5 1 0 M y 1 0 0 5 0 5 1 0 1 0 0 5 webassign net 4 6 0 5 8 1 0

Calculus

DifferentiationS Sketch the region enclosed by the given curves x 9y x 2 7y y 1 0 0 5 0 5 0 1 0 8 6 WebAssign Plot X M y 1 0 0 5 0 5 1 0 1 0 63 0 5 webassign net 0 5 8 1 0

Calculus

DifferentiationSketch a possible graph of a function f that satisfies the following conditions 1 f x 0 on 5 f x 0 on 5 ii f x 0 on 10 and 10 o f x 0 on 10 10 iii lim f x 3 lim f x 0 24 248 20 18 16 14 12 10 8 8 10 12 14 16 18 20

Calculus

DifferentiationConsider the function below f x 5x tan x T 2 x 2 a Find the vertical asymptote s Enter your answers as a comma separated list If an answer does not exist enter DNE Find the horizontal asymptote s Enter your answers as a comma separated list If an answer does not exist enter DNE y b Find the interval where the function is increasing Enter your answer using interval notation Find the interval where the function is decreasing Enter your answer using interval notation c Find the local maximum and minimum values If an answer does not exist enter DNE local maximum value local minimum value d Find the interval where the function is concave up Enter your answer using interval notation

Calculus

Differentiationrm is Consider the convergence divergence of the following series whose nth an n 1

Calculus

DifferentiationFind the number c that satisfies the conclusion of the Mean Value Theorem on the given interval Ente your answers as a comma separated list If an answer does not exist enter DNE f x 0 9 C Graph the function the secant line through the endpoints and the tangent line at c f c 3 2 1 2 16 8 KEN

Calculus

DifferentiationProblem 4 Evaluate the following integral 1 2 100 Problem 4 dx Enter your answer as a sym function of x as in these examples

Calculus

DifferentiationProblem 5 Find the remainder after performing the following divis 11x 5x x 5 Problem 5

Calculus

DifferentiationLet A z f t dt with f x shown in the graph below 0 st 4 3 2 1 2 3 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6

Calculus

DifferentiationGiven At what value of x does the local max of f x occur x f x S a At what value of a does the local min of f x occur x t 5t 24 1 cos t dt

Calculus

DifferentiationFor f x y A x Bx y Cy what values of A B and C give f x y a local maximum value of 17 at the point 10 2 A B C i i Bul i

Calculus

DifferentiationT S S Sketch the region enclosed by the given curves y 3 x y 12x Y 3 6 1 y 8 2 X 0 3 4 82 M 6 th y 8 JS Secti MacBook Air 2 dh 3

Calculus

DifferentiationFind the extreme values of the function and where they occur 17 y 1 x2 1 A None B Local maximum at 0 1 C Local maximum at 1 0 local minimum at 1 0 D Local maximum at 1 0 local minimum at 1 0

Calculus

DifferentiationAre the following functions derivable at the given point If so calculate the derivative f x g x x if x 0 200 if x 0 sin x x in x if x 0 if x 0 0 in x 0

Calculus

DifferentiationCalculate the following derivatives using the definition f x 3x on x 3 g x 4x on x 1 h x 2x 5x on x 1 k x 4x on x 2

Calculus

DifferentiationFind the standard form of the equation of the ellipse with the given characteristics Center 2 9 a 3c foci 5 9 9 9

Calculus

DifferentiationWrite the first five terms of the sequence defined recursively a 27 ak 1 ak 4 a1 a a3 34 a5 Use the pattern to write the nth term of the sequence as a function of n Assume that n begins with 1 an