Mobius 5 assignment PDF

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Mobius 5 assignment...

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Assignment Worksheet

Online Homework System

10/26/19 - 1:21:58 PM EDT

Name:

____________________________

Class:

MAT 1330 - Fall 2019 - All sections

Class #:

____________________________

Section #:

____________________________

Instructor: Benoit Dionne

Assignment: Assignment 5

Question 1: (1 point) If

then its fifth derivative is

__________

Question 2: (1 point) Find the equation of the tangent line to the curve

at the point

. (Hint: simplify before differentiating.) Your answer must be an equation of the form

Question 3: (1 point) Let

a) Given that

can be written in the form

What are the coefficients __________ __________ __________ __________

,

,

, and

?

b) Using the correct answer to (a), and implicit differentiation, find the value of Answer: __________

when

.

.

Question 4: (1 point) Find the derivative of the function

and then evaluate it at

.

__________ .

Question 5: (1 point) Consider the function

What is its derivative at Answer:

?

__________.

(Your answer must be exact and thus may include commands like sqrt and / ; do not give a decimal approximation.)

Question 6: (1 point) Consider the function

Compute the derivative of Answer :

at

.

__________

(Your answer must be exact and thus may include commands like sqrt and / if needed; do not give a decimal approximation.)

Question 7: (1 point) Find the derivative of

__________

Question 8: (1 point) Find an equation of the tangent line to the curve

at the point

. Express your answer in the form

.

Question 9: (1 point) Suppose that

for all Answer:

is a differentiable function that satisfies

. Knowing that

, find

. Provide the exact value.

__________

Hint: Use implicit differentiation. If two differentiable functions are equal for all , then so are their derivatives.

Question 10: (1 point) Let

Use implicit differentiation to find a formula for

Your answer can be a function of both

and .

__________.

Question 11: (1 point) Consider the function

given by

Find the three critical numbers ).

of

and list their exact values in the first column of the table below (in ascending order :

The second column consists of several drop-down menus. Do the following: for each of the intervals of defined by these points, select the phrase that best describes the behaviour of the function interval; for each of the critical numbers, select the phrase that best describes their nature; for each of , select the phrase that best describes the corresponding limiting behaviour of . Behavior __________ __________ __________

__________ __________

__________

__________ __________

__________

__________ __________ __________

on that

Question 12: (1 point) We wish to sketch the graph of the function

Find all the critical numbers of ascending order : ).

and of

. There are two of them; enter their exact values in the first column of the table below (in

The second column consists of several drop-down menus. Do the following: for each of the intervals of defined by these points, select the phrase that best describes the behaviour and shape of the graph of the function ; for each of the critical numbers, select the phrase that best describes their nature; for each of , select the phrase that best describes the corresponding limiting behaviour of . behavior __________ __________ __________

__________ __________

__________

__________ __________ __________

Question 13: (1 point) Consider the function

given by

Find all the critical numbers of and of . There are three of them; enter their approximate values, correct to at least two decimal places, in the first column of the table below (in ascending order : ). The second column consists of several drop-down menus. Do the following: for each of the intervals of defined by these points, select the phrase that best describes the behaviour and shape of the graph of the function ; for each of the critical numbers, select the phrase that best describes their nature; for each of and , select the phrase that best describes the corresponding limiting behaviour of . behavior __________ __________ ____________ __________ __________ ____________

__________ __________

____________

__________ __________ __________...