MA302 Grantham Week 3 Calculus Functions and Graphs Practice Assignment
Question Description
Assignment Submission
For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.
Assignment Scoring
Your last submission is used for your score.
Consider the following function and graph.f(x) = 3
x 
x^{2} − 9 
Determine whether f(x) approaches ∞ or ∞ as x approaches 3 from the left and from the right.
(a)  lim x→3^{−} f(x) 
(b)  lim x→3^{+} f(x) 
2.–/11 pointsLarCalc11 1.5.011.
My NotesConsider the following function.f(x) =
1 
x^{2} − 16 
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.

3.–/1 pointsLarCalc11 1.5.040.
My NotesFind the onesided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (−1/2)^{+}
6x^{2} + x − 1 
10x^{2} − 5x − 5 
4.–/1 pointsLarCalc11 1.5.041.
My NotesFind the onesided limit (if it exists). (If the limit does not exist, enter DNE.)lim x→0^{−}
5 
x 
5.–/1 pointsLarCalc11 1.5.046.
My NotesFind the onesided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (π/2)^{+}
−8 
cos x 
6.–/1 pointsLarCalc11 2.1.010.
My NotesFind the slope of the tangent line to the graph of the function at the given point.
g(x) =  7  x + 7, (6, 0) 
6 
7.–/1 pointsLarCalc11 2.1.021.
My NotesFind the derivative of the function by the limit process.f(x) = x^{2} + x − 5
f '(x) =
8.–/1 pointsLarCalc11 2.1.025.
My NotesFind the derivative of the function by the limit process.f(x) =
7 
x − 8 
f '(x) =
9.–/1 pointsLarCalc11 2.1.038.
My NotesFind an equation of the line that is tangent to the graph of f and parallel to the given line.
Function  Line  
f(x) = 2x^{2}  4x − y + 1 = 0 
10.–/1 pointsLarCalc11 2.2.013.
My NotesUse the rules of differentiation to find the derivative of the function.f(x) =
4  x 
11.–/1 pointsLarCalc11 2.2.017.
My NotesUse the rules of differentiation to find the derivative of the function.f(t) = 5t^{2} + 4t + 1
f '(t) =
12.–/1 pointsLarCalc11 2.2.026.
My NotesUse the rules of differentiation to find the derivative of the function.y = 3x^{4} + 8 sin x
y' =
13.–/4 pointsLarCalc11 2.2.027.
My NotesComplete the table to find the derivative of the function.
Original Function  Rewrite  Differentiate  Simplify  
y =
 x^{} 


14.–/1 pointsLarCalc11 2.2.035.
My NotesFind the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.
Function  Point 
y = (8x + 2)^{2},  (0, 4) 
y'(0) =
15.–/1 pointsLarCalc11 2.2.041.
My NotesFind the derivative of the function.
g(t) = t^{2} −  4 
t^{3} 
16.–/1 pointsLarCalc11 2.2.043.
My NotesFind the derivative of the function.
f(x) =  x^{3} − 3x^{2} + 9 
x^{2} 
17.–/1 pointsLarCalc11 2.2.049.
My NotesFind the derivative of the function.
f '(x) =
18.–/2 pointsLarCalc11 2.2.055.
My NotesConsider the given function and point.
f(x) = −8x^{4} + 11x^{2} − 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.
19.–/7 pointsLarCalc11 2.2.095.
My NotesA silver dollar is dropped from the top of a building that is 1398 feet tall. Use the position function below for freefalling objects.s(t) = −16t^{2} + v_{0}t + s_{0}
(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.)
20.–/1 pointsLarCalc11 2.3.009.MI.
My NotesUse the Product Rule to differentiate the function.
f(x) = x^{3 }cos(x)
21.–/1 pointsLarCalc11 2.3.011.
My NotesUse the Quotient Rule to find the derivative of the function.f(x) =
x 
x − 4 
f '(x) =
22.–/2 pointsLarCalc11 2.3.017.
My NotesFind f '(x)
andf '(c).
Function  Value of c 
f(x) = (x^{3} + 2x)(3x^{4} + 3x − 2)  c = 0 
f '(x) = 

f '(c) = 
23.–/2 pointsLarCalc11 2.3.022.
My NotesFind f '(x) and f '(c).
Function  Value of c  
f(x) =
 c =

f '(x)  = 

f '(c)  = 

24.–/4 pointsLarCalc11 2.3.025.MI.SA.
My NotesThis 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 
13x^{4} 
25.–/1 pointsLarCalc11 2.3.029.
My NotesFind the derivative of the function.
f(x) =
4 − 5x − x^{2} 
x^{2} − 6 
26.–/1 pointsLarCalc11 2.3.033.
My NotesFind the derivative of the function.f(x) =
9x − 1  

27.LarCalc11 2.3.041.
My NotesQuestion Part 
Points 
Submissions Used 
Find the derivative of the trigonometric function.f(t) = t^{9} sin(t)
f '(t) =
28.LarCalc11 2.3.043.
My NotesQuestion Part 
Points 
Submissions Used 
Find the derivative of the trigonometric function.
f(t) =  cos(t) 
t 
29.LarCalc11 2.3.049.
My NotesQuestion Part 
Points 
Submissions Used 
Find the derivative of the trigonometric function.y =
5(1 − sin(x)) 
2 cos(x) 
y' =
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