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Rogawski - Calculus 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 16 / 28

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

Last Saved : n/a Saving...  ()

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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Total
16/28 (57.1%)

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    W. H. Freeman and WebAssign





    W. H. Freeman and WebAssign have partnered to deliver an outstanding resource for your calculus course.

    Combining the mostly widely used online homework platform and a new textbook that presents calculus with a solid mathematical precision but with everyday sensibility that puts the main concepts in clear terms, Rogawski's Calculus is rigorous without being inaccessible and clear without being too informal-it has the perfect balance for instructors and their students.

    WebAssign Premium for Rogawski's Calculus, Second Edition will have approximately 5000 questions with solutions available to students by instructor choice. In addition to these questions, it offers CalcClip tutorial videos, a fully searchable eBook linked to questions as well as optional algorithmic solutions.

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1. –/3 points RogaCalcET2 2.4.023.Tutorial. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Determine the point of discontinuity.
f(x) = 
x + 1
5x − 4
x =

State the type of discontinuity.
    

State whether the function is left- or right-continuous.
    
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2. –/1 points RogaCalcET2 2.1.013.Tutorial. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Estimate the instantaneous rate of change at the point indicated. (Round your answer to four decimal places.)
y(x) = 
1
x + 2
;    x = 2
rate of change =

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3. –/1 points RogaCalcET2 2.2.017.Tutorial. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Estimate the limit numerically or state that the limit doesn't exist. (Round your answer to four decimal places. If an answer does not exist, enter DNE.)
lim x→49 
x
 − 7
x − 49

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4. –/1 points RogaCalcET2 2.2.034. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Estimate the limit numerically or state that the limit does not exist. (Round your answer to two decimal places. If you need to use or –, enter INFINITY or –INFINITY, respectively. If an answer does not exist, enter DNE.)
lim r → 0 (1 + r)8/r

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5. –/1 points RogaCalcET2 2.3.005.Tutorial. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the limit using the Limit Laws.
lim t → 5 2t−1

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6. –/1 points RogaCalcET2 2.3.013. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the limit using the Limit Laws.
lim t → 8 
−5t + 7
t + 2
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7. –/2 points RogaCalcET2 2.4.004.Tutorial. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Consider the graph of a function g(x).
WebAssign Plot
Find the point c at which the function has a jump discontinuity but is right-continuous.
c =

What value should be assigned to g(c) to make g left-continuous at x = c?
g(c) =

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8. –/1 points RogaCalcET2 2.4.073. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the limit using the substitution method.
lim x→3 x−3/2
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9. –/2 points RogaCalcET2 2.5.013.Tutorial. My Notes
Question Part
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1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Decide if the following limit exists.
lim x→4 
5x2 − 16x − 16
2x2 − 32
    

If the limit exists, evaluate it. (If an answer does not exist, enter DNE.).

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10. –/1 points RogaCalcET2 2.5.024. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the limit or state that it does not exist. (If an answer does not exist, enter DNE.)
lim x→9 
10 − x
 − 1
3 − 
x
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11. –/2 points RogaCalcET2 2.6.006.Tutorial. My Notes
Question Part
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1 2
–/1 –/1
0/50 0/50
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–/2
 
Plot the graphs of
u(x) = 3 + 
x − 
π
2
 and
l(x) = 3 sin x
 on the same set of axes.


Compute
lim x→π/2 f(x)
 if f(x) is squeezed by
l(x) and u(x) at x = 
π
2
.

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12. –/1 points RogaCalcET2 2.7.008.Tutorial. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the limit.
lim x→∞ 
4x2 + 11x
5x2 + 12

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13. –/1 points RogaCalcET2 2.8.005.Tutorial. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Using the Intermediate Value Theorem, does the equation
cos 6x = 2x
 have a solution in the interval [0, 1]?
    

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14. –/1 points RogaCalcET2 2.9.004.Tutorial. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Consider
lim x→4 f(x),
 where
f(x) = 3x − 4.
 Find a δ such that
|f(x) − 8| < 0.007 if |x − 4| < δ.
(Round your answer to six decimal places.)
δ =

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15. –/9 points RogaCalcET2 2.1.007.Tutorial. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/9
 
With an initial deposit of $100, the balance in a bank account after t years is
f(t) = 100(1.18)t dollars.

What are the units of the rate of change of f(t)?
    

Find the average rate of change over [0, 0.5] and [0, 1]. (Round your answers to two decimal places.)
[0, 0.5] =
[0, 1] =

Estimate the instantaneous rate of change at t = 0.5 by computing the average rate of change over intervals to the left and right of t = 0.5. (Round your answers to four decimal places.)
Interval [0.5, 0.51] [0.5, 0.501] [0.5, 0.5001]
Average rate of change    
Interval [0.49, 0.5] [0.499, 0.5] [0.4999, 0.5]
Average rate of change    

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