MA302 Grantham Week 3 Calculus Functions and Graphs Practice Assignment

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Consider the following function and graph.f(x) = 3

x
x2 − 9

Maple Generated Plot

Determine whether f(x) approaches ∞ or -∞ as x approaches 3 from the left and from the right.
(a)lim x3 f(x)



(b)

lim x3+ f(x)

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2./11 pointsLarCalc11 1.5.011.Ask Your Teacher

My Notes

Consider the following function.f(x) =

1
x2 − 16
Complete the following table. (Round your answers to two decimal places.)
x

−4.5

−4.1

−4.01

−4.001

−4

−3.999

−3.99

−3.9

−3.5

f(x)

?

Use the table to determine whether f(x) approaches ∞ or −∞ as x approaches

−4

from the left and from the right.

lim x−4 f(x) =

lim x−4+ f(x) =



Use a graphing utility to graph the function to confirm your answer.


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3./1 pointsLarCalc11 1.5.040.Ask Your Teacher

My Notes

Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (−1/2)+

6x2 + x − 1
10x2 − 5x − 5

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4./1 pointsLarCalc11 1.5.041.Ask Your Teacher

My Notes

Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)lim x0

6 +
5
x

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5./1 pointsLarCalc11 1.5.046.Ask Your Teacher

My Notes

Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (π/2)+

−8
cos x

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6./1 pointsLarCalc11 2.1.010.Ask Your Teacher

My Notes

Find the slope of the tangent line to the graph of the function at the given point.

g(x) =7x + 7, (-6, 0)
6

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7./1 pointsLarCalc11 2.1.021.Ask Your Teacher

My Notes

Find the derivative of the function by the limit process.f(x) = x2 + x − 5

f '(x) =

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8./1 pointsLarCalc11 2.1.025.Ask Your Teacher

My Notes

Find the derivative of the function by the limit process.f(x) =

7
x − 8

f '(x) =

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9./1 pointsLarCalc11 2.1.038.Ask Your Teacher

My Notes

Find an equation of the line that is tangent to the graph of f and parallel to the given line.

FunctionLine
f(x) = 2x2

4xy + 1 = 0

y =

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10./1 pointsLarCalc11 2.2.013.Ask Your Teacher

My Notes

Use the rules of differentiation to find the derivative of the function.f(x) =

4x
f '(x) =

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11./1 pointsLarCalc11 2.2.017.Ask Your Teacher

My Notes

Use the rules of differentiation to find the derivative of the function.f(t) = 5t2 + 4t + 1

f '(t) =

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12./1 pointsLarCalc11 2.2.026.Ask Your Teacher

My Notes

Use the rules of differentiation to find the derivative of the function.y = 3x4 + 8 sin x

y' =

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13./4 pointsLarCalc11 2.2.027.Ask Your Teacher

My Notes

Complete the table to find the derivative of the function.

Original FunctionRewriteDifferentiateSimplify
y =
3
5x4

x

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14./1 pointsLarCalc11 2.2.035.Ask Your Teacher

My Notes

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

FunctionPoint
y = (8x + 2)2, (0, 4)

y'(0) =

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15./1 pointsLarCalc11 2.2.041.Ask Your Teacher

My Notes

Find the derivative of the function.

g(t) = t24
t3
g'(t) =

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16./1 pointsLarCalc11 2.2.043.Ask Your Teacher

My Notes

Find the derivative of the function.

f(x) = x3 − 3x2 + 9
x2
f '(x) =

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17./1 pointsLarCalc11 2.2.049.Ask Your Teacher

My Notes

Find the derivative of the function.$ f(x) = \sqrt{x} - {\color{red}7}\sqrt[3]{x}$

f '(x) =

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18./2 pointsLarCalc11 2.2.055.Ask Your Teacher

My Notes

Consider the given function and point.

f(x) = −8x4 + 11x2 − 3,(1, 0)

(a)

Find an equation of the tangent line to the graph of the function at the given point.

y =

(b)

Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results.


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19./7 pointsLarCalc11 2.2.095.Ask Your Teacher

My Notes

A silver dollar is dropped from the top of a building that is 1398 feet tall. Use the position function below for free-falling objects.s(t) = −16t2 + v0t + s0

(a) Determine the position and velocity functions for the coin.

s(t) =
v(t) =


(b) Determine the average velocity on the interval [1, 2].
ft/s



(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.

v(1) = ft/s
v(2) = ft/s

(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)
t = s



(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)

ft/s

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20./1 pointsLarCalc11 2.3.009.MI.Ask Your Teacher

My Notes

Use the Product Rule to differentiate the function.
f(x) = x3 cos(x)

f '(x) =

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21./1 pointsLarCalc11 2.3.011.Ask Your Teacher

My Notes

Use the Quotient Rule to find the derivative of the function.f(x) =

x
x − 4

f '(x) =

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22./2 pointsLarCalc11 2.3.017.Ask Your Teacher

My Notes

Find f '(x)

and

f '(c).

FunctionValue of c
f(x) = (x3 + 2x)(3x4 + 3x − 2) c = 0

f '(x) =

f '(c) =

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23./2 pointsLarCalc11 2.3.022.Ask Your Teacher

My Notes

Find f '(x) and f '(c).

FunctionValue of c
f(x) =
sin x
x

c =

π
6

f '(x)

=

f '(c)

=

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24./4 pointsLarCalc11 2.3.025.MI.SA.Ask Your Teacher

My Notes

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

Find the derivative of the function without using the Quotient Rule.

15
13x4

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25./1 pointsLarCalc11 2.3.029.Ask Your Teacher

My Notes

Find the derivative of the function.
f(x) =

4 − 5xx2
x2 − 6
f '(x) =

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26./1 pointsLarCalc11 2.3.033.Ask Your Teacher

My Notes

Find the derivative of the function.f(x) =

9x − 1
x
f '(x) =

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27./1 pointsLarCalc11 2.3.041.Ask Your Teacher

My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.f(t) = t9 sin(t)

f '(t) =

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28./1 pointsLarCalc11 2.3.043.Ask Your Teacher

My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.

f(t) = cos(t)
t
f '(t) =

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29./1 pointsLarCalc11 2.3.049.Ask Your Teacher

My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.y =

5(1 − sin(x))
2 cos(x)

y' =

Tutor Answer

vmohanakumar
School: Carnegie Mellon University

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Anonymous
awesome work thanks

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