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Hughes-Hallett et al-Calculus: Single & Multivar 6 (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 23

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Calculus: Single and Multivariable 6/e by Deborah Hughes-Hallett, Andrew M. Gleason, and William G. McCallum published by John Wiley & Sons, Inc. is now a WebAssignPLUS selection. WebAssignPLUS includes a complete on-line version of the text and a variety of interactive study aids. All of these rich resources are linked together in a dynamic and interactive environment for students. Additional links to the eBook within each problem are structured to support the way students work and provide them with superior just-in-time learning resources. Also the eBook availability provides students with a significantly less expensive option than the printed version.

    Also included with this WebAssignPLUS selection
    • eBook access available from each question, and from a dynamic table of contents
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    In this assignment we present several textbook question types found in Chapter 3 on Short-cuts to Differentiation. Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. 1/1 points  |  Previous Answers HHCalc6 3.1.036. My Notes
Question Part
Points
Submissions Used
1
1/1
3/50
Total
1/1
 
Find the derivative of the given function.
h(t) = 
8
t
 + 
3
t2
h'(t) =
−8t2​−6t3​
Correct: Your answer is correct.

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2. –/2 points HHCalc6 3.1.065. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
If
f(x) = (5x + 12)(3x − 8), find f '(x)
 and
f ''(x).
f '(x) = 
f ''(x) = 

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3. –/1 points HHCalc6 3.2.039. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
With a yearly inflation rate of 9%, prices are given by
P(t) = P0(1.09)t,
where
P0
 is the price in dollars when
t = 0
 and t is time in years. Suppose
P0 = 1.
 How fast (in cents/year) are prices rising when
t = 10?
 (Round your answer to two decimal places.)
¢/yr

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4. –/1 points HHCalc6 3.3.045. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the equation of the tangent line to the graph of
f(x) = 
2x − 4
x + 1
 at the point at which
x = 0.
 (Let x be the independent variable and y be the dependent variable.)

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5. –/1 points HHCalc6 3.4.048. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the derivative.
z = (te4t + e7t)5
dz
dt
 =

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6. 0/3 points  |  Previous Answers HHCalc6 3.4.057. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 0/1 –/1
0/50 1/50 0/50
Total
0/3
 
Use the figure below and the chain rule to estimate the derivative. The graph of
f(x)
 has a sharp corner at
x = 2.
Let
h(x) = f(g(x)).
 Find the following. (If an answer does not exist, enter DNE.)
(a)    
h'(1) =


(b)    
h'(2) = Incorrect: Your answer is incorrect.


(c)    
h'(3) =

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7. –/3 points HHCalc6 3.5.062. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
The metal bar of length l in the figure below has one end attached at the point P to a circle of radius a. Point Q at the other end can slide back and forth along the x-axis.
(a) Find x as a function of θ.
x =


(b) Assume lengths are in centimeters and the angular speed (dθ/dt) is 4 radians/second counterclockwise. Find the speed at which the point Q is moving when the following occurs.
(i)    
θ = π/2
cm/sec

(ii)    
θ = π/4
cm/sec

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8. –/1 points HHCalc6 3.6.032. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the derivative. It may be to your advantage to simplify before differentiating.
f(x) = cos(arctan 4x)
f '(x) =

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9. –/1 points HHCalc6 3.7.025. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the slope of the tangent to the curve at the point specified.
x3 + 5x2y + 2y2 = 13y + 1
 at
(1, 4)

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10. –/1 points HHCalc6 3.8.019. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Use the definitions of
sinh x
 and
cosh x
 to find an identity for
(sinh x)(cosh x).
    

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11. –/4 points HHCalc6 3.9.027. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
Total
–/4
 
The following question investigates the motion of a projectile shot from a cannon. The fixed parameters are the acceleration of gravity,
g = 9.8 m/sec2,
 and the muzzle velocity,
v0 = 600 m/sec,
 at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary.

The range of the projectile is
f(θ) = 
v02
g
 sin 
πθ
90
wq = 36735 sin 
πθ
90
 meters.
(a) Find the range with
θ = 30°.
 (Round your answer to the nearest integer.)
m

(b) Find a linear function of θ that approximates the range for angles near 30°. (Round all numerical values to the nearest integer.)
f(θ) ≈


(c) Find the range for 31°. (Round your answer to the nearest integer.)
m

Find the range for 31° using the approximation from part (b). (Round your answer to the nearest integer.)
m

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12. –/3 points HHCalc6 3.10.011. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Applying the Mean Value Theorem with
a = 1, b = 11
 to the function in the figure below leads to the point c shown.
(1,  
  6)
(11,  
  5)
What is the value of
f '(c)?
f '(c) =


What can you say about the values of
f '(x1) and f '(x2)?
From the graph, we conclude that
f '(x1)
f '(c)
 and
f '(x2)
f '(c).

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13. –/1 points HHCalc6 3.R.074. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Assume that y is a differentiable function of x and find
dy/dx.
x5 + y5 − 8x4y = 0
dy/dx =

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