Differentiation Questions and Answers

4 3 x2 Find the derivative

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

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

Question 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

Simplify the expression as much as possible cos t 1 sin t N help formulas

Evaluate 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

Calculate the binomial coefficient 11CB

Find 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

Solve the exponential equation 3x 9 X

Solve 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

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

Find f f x 20x 12x 6 f x Question Help Message instructor f 0 2 f 1 0

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

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

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

Find the exact value of each expression 34 cos 1 35 sin 3 2

Use 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

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

VE vo X Simplify into a single log 2 log x log 4y

X Given that f x 3x 4 and g x x 1 find g f x 76 El

Question 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

2 Evaluate x x 1dx the integral

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

y 19 cos 4x 6 Amplitude Period Phase shift F C

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

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

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

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

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

rm 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

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

Problem 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

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

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

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

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

Evaluate the definite integral 8 X

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

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

Find 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

Write 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