Differentiation Questions and Answers
![6 Which substitution will you make to evaluate the indefinite integ x 1 dx x 4x a x 1 b x 4x c x 1 x 4x](https://media.kunduz.com/media/sug-question-candidate/20231207184002678877-5061986.jpg?w=256)
Calculus
Differentiation6 Which substitution will you make to evaluate the indefinite integ x 1 dx x 4x a x 1 b x 4x c x 1 x 4x
![4 3 x2 Find the derivative](https://media.kunduz.com/media/sug-question-candidate/20231207081251599880-6056134.jpg?w=256)
![27 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](https://media.kunduz.com/media/sug-question-candidate/20231207020830228818-4582308.jpg?w=256)
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
![Consider 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](https://media.kunduz.com/media/sug-question-candidate/20231206234146275799-4971328.jpg?w=256)
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
![Question Evaluate the indefinite integral given below Provide your answer below X5 x 2 dx](https://media.kunduz.com/media/sug-question-candidate/20231206202008833405-6031580.jpg?w=256)
Calculus
DifferentiationQuestion Evaluate the indefinite integral given below Provide your answer below X5 x 2 dx
![Evaluate the indefinite integral given below using the indicated substitution 3 4 42 x 3a 2 da U 3x x Provide your answer below](https://media.kunduz.com/media/sug-question-candidate/20231206201157322021-6031580.jpg?w=256)
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
![Simplify the expression as much as possible cos t 1 sin t N help formulas](https://media.kunduz.com/media/sug-question-candidate/20231206200344370094-4704102.jpg?w=256)
![Evaluate the indefinite integral given below using the indicated substitution fa Provide your answer below 17 8x dx u 17 8x](https://media.kunduz.com/media/sug-question-candidate/20231206195206016644-6031580.jpg?w=256)
Calculus
DifferentiationEvaluate the indefinite integral given below using the indicated substitution fa Provide your answer below 17 8x dx u 17 8x
![Calculate the binomial coefficient 16C15](https://media.kunduz.com/media/sug-question-candidate/20231206194511814159-5836419.jpg?w=256)
![Calculate the binomial coefficient 11CB](https://media.kunduz.com/media/sug-question-candidate/20231206194455150006-5836419.jpg?w=256)
![Find the area of the triangle having the indicated angle and sides Round your a B 125 a 94 c 39](https://media.kunduz.com/media/sug-question-candidate/20231206194311607107-5836419.jpg?w=256)
Calculus
DifferentiationFind the area of the triangle having the indicated angle and sides Round your a B 125 a 94 c 39
![Use 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](https://media.kunduz.com/media/sug-question-candidate/20231206194221952620-5836419.jpg?w=256)
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
![Solve the exponential equation 3x 9 X](https://media.kunduz.com/media/sug-question-candidate/20231206194040845861-5836419.jpg?w=256)
![Solve the logarithmic equation Round your answer to three decimal places log10 x 1133 X 1](https://media.kunduz.com/media/sug-question-candidate/20231206194112628934-5836419.jpg?w=256)
Calculus
DifferentiationSolve the logarithmic equation Round your answer to three decimal places log10 x 1133 X 1
![Find 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](https://media.kunduz.com/media/sug-question-candidate/20231206193925558864-5836419.jpg?w=256)
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
![Find 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](https://media.kunduz.com/media/sug-question-candidate/20231206174423202304-5061986.jpg?w=256)
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
![Find f f x 20x 12x 6 f x Question Help Message instructor f 0 2 f 1 0](https://media.kunduz.com/media/sug-question-candidate/20231206174619424526-5061986.jpg?w=256)
![Orphof 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](https://media.kunduz.com/media/sug-question-candidate/20231206160513233773-6011704.jpg?w=256)
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
![Example 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](https://media.kunduz.com/media/sug-question-candidate/20231206062234055800-6056134.jpg?w=256)
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
![7 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](https://media.kunduz.com/media/sug-question-candidate/20231206055010550165-5923485.jpg?w=256)
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
![Find the exact value of each expression 34 cos 1 35 sin 3 2](https://media.kunduz.com/media/sug-question-candidate/20231206045707050342-4582308.jpg?w=256)
![Use the Laws of Logarithms to expand the expression log V 7x y 1 1 9 log 7 x log 7 y](https://media.kunduz.com/media/sug-question-candidate/20231206031752268758-4426152.jpg?w=256)
Calculus
DifferentiationUse the Laws of Logarithms to expand the expression log V 7x y 1 1 9 log 7 x log 7 y
![The bounded area between the curves f x 15x4 and g x 15x is Your answer should be a number](https://media.kunduz.com/media/sug-question-candidate/20231205193513528394-6331536.jpg?w=256)
Calculus
DifferentiationThe bounded area between the curves f x 15x4 and g x 15x is Your answer should be a number
![Find the area of the triangle determined by the points P Q R P 1 1 2 Q 2 0 1 R 0 2 1](https://media.kunduz.com/media/sug-question-candidate/20231204221727954408-4724413.jpg?w=256)
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
![VE vo X Simplify into a single log 2 log x log 4y](https://media.kunduz.com/media/sug-question-candidate/20231204182606621622-5472891.jpg?w=256)
![X Given that f x 3x 4 and g x x 1 find g f x 76 El](https://media.kunduz.com/media/sug-question-candidate/20231204181109961481-5472891.jpg?w=256)
![Question 1 Solve the given inequality Enter your answer using interval notation and exact values 2x 724x 3](https://media.kunduz.com/media/sug-question-candidate/20231204012517123738-3712867.jpg?w=256)
Calculus
DifferentiationQuestion 1 Solve the given inequality Enter your answer using interval notation and exact values 2x 724x 3
![Next 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](https://media.kunduz.com/media/sug-question-candidate/20231203160836001482-3712867.jpg?w=256)
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
![2 Evaluate x x 1dx the integral](https://media.kunduz.com/media/sug-question-candidate/20231203092037183651-5366129.jpg?w=256)
![a 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](https://media.kunduz.com/media/sug-question-candidate/20231203050227780925-5923485.jpg?w=256)
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
![y 19 cos 4x 6 Amplitude Period Phase shift F C](https://media.kunduz.com/media/sug-question-candidate/20231202022016312838-4704102.jpg?w=256)
![The 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](https://media.kunduz.com/media/sug-question-candidate/20231202015913303151-5868017.jpg?w=256)
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
![t 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](https://media.kunduz.com/media/sug-question-candidate/20231201191701703876-5886119.jpg?w=256)
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
![S 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](https://media.kunduz.com/media/sug-question-candidate/20231201191241700460-5886119.jpg?w=256)
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
![Sketch 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](https://media.kunduz.com/media/sug-question-candidate/20231201154534205674-5061986.jpg?w=256)
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
![Consider 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](https://media.kunduz.com/media/sug-question-candidate/20231201154108198692-5061986.jpg?w=256)
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
![rm is Consider the convergence divergence of the following series whose nth an n 1](https://media.kunduz.com/media/sug-question-candidate/20231201164614377243-6319517.jpg?w=256)
Calculus
Differentiationrm is Consider the convergence divergence of the following series whose nth an n 1
![Find 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](https://media.kunduz.com/media/sug-question-candidate/20231201153713711382-5061986.jpg?w=256)
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
![Problem 4 Evaluate the following integral 1 2 100 Problem 4 dx Enter your answer as a sym function of x as in these examples](https://media.kunduz.com/media/sug-question-candidate/20231201032417152950-4270279.jpg?w=256)
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
![Problem 5 Find the remainder after performing the following divis 11x 5x x 5 Problem 5](https://media.kunduz.com/media/sug-question-candidate/20231201030223222180-4270279.jpg?w=256)
Calculus
DifferentiationProblem 5 Find the remainder after performing the following divis 11x 5x x 5 Problem 5
![Let 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](https://media.kunduz.com/media/sug-question-candidate/20231201003329412743-5868017.jpg?w=256)
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
![Given 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](https://media.kunduz.com/media/sug-question-candidate/20231201003314695035-5868017.jpg?w=256)
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
![For 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](https://media.kunduz.com/media/sug-question-candidate/20231130193928960913-5941274.jpg?w=256)
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
![T 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](https://media.kunduz.com/media/sug-question-candidate/20231130190440150371-5886119.jpg?w=256)
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
![Find 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](https://media.kunduz.com/media/sug-question-candidate/20231130192409368372-6051355.jpg?w=256)
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
![Evaluate the definite integral 8 X](https://media.kunduz.com/media/sug-question-candidate/20231130190221593508-5886119.jpg?w=256)
![Are 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](https://media.kunduz.com/media/sug-question-candidate/20231130170824835140-6167964.jpg?w=256)
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
![Calculate 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](https://media.kunduz.com/media/sug-question-candidate/20231130160252610234-6167964.jpg?w=256)
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
![Find the standard form of the equation of the ellipse with the given characteristics Center 2 9 a 3c foci 5 9 9 9](https://media.kunduz.com/media/sug-question-candidate/20231129212238930466-5836419.jpg?w=256)
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
![Express x eliminating ln 3t y 2 t in the form y f x by the parameter y](https://media.kunduz.com/media/sug-question-candidate/20231129224758870689-4971328.jpg?w=256)