Differentiation Questions and Answers

Find the derivative of the function given below without using the Quotient or the Product Rules Type your solution step by step 1 xe x f x

S b f x x cos x COS 24

3 Find the derivative of each function y x x 4 a y

State the common difference then list the next three terms of each arithmetic sequence a 48 43 38 33 b 8 8 24 40 c 1 1 1 d d d Enter your responses in the space provided Be sure to include a b and c in your responses to indicate the answer for each 27 4

Choose the correct match for tan x cot x Select one O a 2 sec x O b sec x csc x O c O d 2 cot x sec x sec x CSC X

Given that I 10 12 watts meter2 what is the intensity of a sound for which the decibel level of the sound measures 113 Round off your answer to three decimal places Keypa

Eva invests 6700 in a new savings account which earns 5 8 annual interest compounded continuously What will be the value of her investment after 3 years Round to the nearest cent

5 points Find the 4 second partial derivatives of g u v tan u Just state your answers You must use correct notation to receive full credit Fyi that s inverse tangent

Show the following vector field is conservative Then find its potential function F 2e cos y 2e sin y Show all steps

Given z V 2x 3y x st y t s find and using the chain rule for 2 independent variables Show all steps

Tessa has recently inherited 9700 which she wants to deposit into an IRA account She has determined that her two best bets are an account that compounds annually at an annual rate of 4 6 Account 1 and an account that compounds semi annually at an annual rate of 2 9 Account 2 Step 1 of 2 Which account would pay Tessa more interest nh

The half life of radium 226 is approximately 1 600 years Step 1 of 3 Determine a so that A t Apa describes the amount of radium 226 left after t years where Ag is the amount at times 0 Round to six decimal places Answer Keys

25x 9y 225 a Find the standard form of the equation of the hyperbola If the hyperbola is degenerate enter NONE in each answer blank b Find the center vertices and foci of the hyperbola center x y vertices x y 1 x y foci x y x y 15 10 5 15 Find the asymptotes of the hyperbola Enter your answers as a comma separated list of equations 10 smaller x value c Sketch the hyperbola Use a graphing utility to verify your answer y 5 15 10 5 10 15 10 larger x value 151 smaller x value larger x value y 15 10 5 10 15 y 5 10

ou want to estimate the first derivative of f x given values of the function at discrete points x1 x2 n Which of these formulas is appropriate for estimating f xo Select all that are orrect a f x b f x c f x 3f xi 4f xi 1 f xi 2 2h f xi 1 f xi 1 2h 3f xi 4f 2i i f 2 2 2 h

Eva invests 5400 in a new savings account which earns 5 2 annual interest compounded monthly What will be the value of her investment after 6 years Round to the nearest cent inte f

2 For each function find the derivative using the definition lim h 0 a f x x 2x f x h f x h and evaluate at x 2

18 Sketch the derivative of the following graph m 3 2 C

dy The separable IVP 9y with initial condition y 0 7 has solution da y x

Problem 2 Find two linearly independent power series solutions centered at x 0 for the differential equati y 2ty 2y 0 Write the first three terms of each power series

Select the simplified form of each given expression below os x csc x tan x 2 11 cos x cos 53 12 53 A 1 D tan x sin a 1 cosa A 1 D 2 sec a 1 cot 13 53 1 tan 1 cosa sin a A D sin cos sec B E sin x csc x B 2 sin a E csc a B csc E cot C cos x C 2 csc a C tan

Use the Definition of derivative to calculate f x if x x x 3 menue

Use the Definition of derivative to calculate f x if f x menue For the toolbar press ALT F10 PC or ALT FN F1000 1 x 5

13 The globe ina classroom has a diameter of Cinches which Comentation describes the volumes

The polynomial 2x 3x 5 ho a factor of x 1 what is the other factor

4 If h r is a differentiable function with h 1 2 and h 1 1 evaluate f 1 given that f x h x h x 2 1 5 If blo Answer f 1 9 2

2 If h r is a differentiable function with h 1 2 and h 1 1 evaluate f 1 given that 1 tan x Answer f 1 8 3m 1 4

Find the intervals on which the function f x x sina is increasing or decreasing on interval 27 27

b Verify that the function f x satisfies the conditions of the mean value theorem on the interval 1 9 and find all numbers c in the interval such that f c is equal to the slope of the secant line between 1 f 1 and 9 f 9

an Value Theorem a Find the value s of c guaranteed by the Mean Value Theorem for f x ln x on th 1 4

a Find the critical points of the function f x x 6x 9x 3

Given the matrices A and A find the following AA B where a 8 44 2B where e C The product A B where j b f k C 9 1 d h

combine into one log expression log x 1 log x 1 log x log 3 O log x2 1 3 x O log x 1 3x O log x 1 x 1 3 x O log x 1 3 x Question 23 let f x 3x 5 find an expression for inverse of f x Hind find f x O x 3 5 O 3x 5 O No answer text provided x 51 3

Find equation p x 3x 1 x x 2 Oy 3 Oy 3 Othere is no Horizontal Asymtotes O y 0 Question 12 Use Graphical Calculator to find all zeros for g x x 6x 1 Ox 0 16 x 2 36 Ox 0 16 x 2 36 Ox 0 16 x 2 36 Ox 0 16 x 2 36

2 1 8 none of these answers 0 x 4 O x 1 O x 3 Question 14 Solve for x log x log 2x 3 O none of these answers O x 2 3 O x 3 2 O x 3 Question 15

8 Determine the derivative for f x x

n 1 n 2 Show the derivation of and give the Taylor series for sin x around x 1

3 Find the formula for the Maclaurin series for f x 1 1 x

converge Remember to check endpoints if there is an interval of convergence 5 Find dy for the curve x t lnt y t 1 t What happens as t 0 dx 6 Find the 23

Comparison and order of int 1 State the greatest number plotted on the following number line i 10 i 2 State the smallest number plotted on the following number line 20 a 4 and 8 5 15 a 3 and 6 10 3 For each of the following pairs of numbers Plot the numbers on a number line 0 5 b 17 and 3 4 For each of the following pairs of numbers Plot the numbers on a number line 0 b 7 and 16 5 State the greatest number in each set a 19 13 6 b 16 6 12 e 7 17 12 f 8 8 7 5 c 2 and 7 10 10 c 8 and 5 15 ii State which number is larger 15 c 20 3 15 g 35 36 40 20 ii State which number is smaller d 4 and 9 d 1 and 3 d 13 14 2 h 99 87 71

Solve the following polynomial equation by factoring or using the quadratic formula Identify all solutions x 11x 18 0 Answer 2 Points

10 5 pts Openstax 6 9 394 Calculate dx In sech x tanh x 11 5 pts Openstax 6 9 400 Integrate f tanh x sech x dx

Look at the graph 10 5 Submit 1014 5 0 10 What is the equation of the vertical asymptote X 10

7 Let x t 2 y t 3 4t be parametric equations Determine the interval fort in which the curve is concave up

Use f x lim b 0 x f x h f x h s x 4x 3 to find the derivative at x for the given func

OX 2 Question 2 Find the x intercept and the y intercepts for the function given bel y log x 2 no x intercept and y 2 is the y intercept O x 3 is its x intercept and no y intercept O x 2 is its x intercept and no y intercept

O none of these answers Question 7 Find max point for f x x 6x 1 O 1 4 4 6 O 1 4 4 6 O 1 4 4 6 O none of these answers

In AVWX v 390 inches w 390 inches and x 500 inches Find the measure of ZX to the nearest 10th of a degree

Minimize f x y z x y z subject to 6x 2y 8z 104

Minimize f x y z x y z subject to 4x 8y 6z 116 Y

Find fxx x y fxy x y fyx x y and fyy x y for the following function 2x 5y 6x f x y fxx x y fxy x y 9y 5y 3x