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U. of Florida Math Dept.-Concepts in Calculus 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 18 / 36

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

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10 11 12
–/5 –/2 –/3 –/2 –/8 –/1 –/2 –/3 –/1 –/1 –/1 –/7
Total
18/36 (50.0%)

  • Instructions

    Here are some questions from Concepts in Calculus 1/e by University of Florida Mathematics Department published by Open Resource Textbooks.

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1. –/5 points UFLCalc1 1.3.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50
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–/5
 
Given the graph of f(x) shown, find the following.
WebAssign Plot
(a) What is f(3)?
f(3) =

(b) Solve the equation
f(x) = 0.
 (Enter your answers as a comma-separated list.)
x =


(c) What are the domain and range of f?
Domain:
    

Range:
    

(d) True/False: The pair (0, 2) is on the graph of the relation
x2 + y2 = f(x).
    
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2. –/2 points UFLCalc1 2.8.002. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
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–/2
 
Find a simple transformation, h(x), of g(x) that is identical to f(x) for all points except those indicated. Use this fact to sketch the function f(x).
f(x) = 
3x2 + 10x + 3
x2 + 3x
;  g(x) = 
1
x
;  x = −3
h(x) =

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3. –/3 points UFLCalc1 2.10.009. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Write all horizontal and vertical asymptotes for the function; list any removable discontinuities (holes). (If an answer does not exist, enter DNE.)
f(x) = 
x2 − 3x
x2 − 9
 
vertical asymptote     x =
horizontal asymptote     y =
hole     x =
Help Me Learn By
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4. –/2 points UFLCalc1 2.11.001. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
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–/2
 
Find the equation of the tangent line to the graph of the function
f(x) = x2 + 2x
 at the point
(2, 8).



Sketch both the graph of
f(x)
 and the tangent line on the same axes.
No Solution
Help
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5. –/8 points UFLCalc1 4.24.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
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–/8
 
Suppose that the graph below is the derivative g' of a continuous function g. Determine the following: the intervals on which g is increasing/decreasing, the intervals on which g is concave up/down, the critical numbers, the local extrema, and inflection points for g.
WebAssign Plot
Determine the intervals on which g is increasing/decreasing. (Select all that apply.)
Increasing:


Decreasing:


Determine the intervals on which g is concave up/down. (Select all that apply.)
Concave up:


Concave down:


Determine the critical numbers, the local extrema, and inflection points for g. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
critical numbers     x =
local maximum     x =
local minimum     x =
inflection points     x =
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6. –/1 points UFLCalc1 4.30.002. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the general antiderivative for the function below; assume we have chosen an interval I on which the function is continuous. The function may require an algebraic manipulation first. (Use C for the constant of integration.)
f(x) = π
7
 + ex
F(x) =
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7. –/2 points UFLCalc1 A.7.001. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
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–/2
 
Consider the center and radius given below.
Center
(−2, −1), radius 2

  • Part 1 - Equation

    Find the standard equation of the circle given the center and radius.
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8. –/3 points UFLCalc1 1.5.010.Tut. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Given the graph of
f(x)
 shown, answer the following.
WebAssign Plot
(a) What is
f −1(−2)?


(b) Solve the equation
f(x) = −4.
 What is
f −1(−4)?


(c) Sketch the graph of the inverse function.

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9. –/1 points UFLCalc1 1.5.012.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Use properties of exponents and logarithms to evaluate the expression as a rational number.
log3 
27
 

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10. –/1 points UFLCalc1 1.5.015.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Use properties of exponents and logarithms to evaluate the expression as a rational number.
eln(3) − ln(2)

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11. –/1 points UFLCalc1 1.5.018.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Write the expression below so that only a single logarithm or exponential function appears. (Reduce to exact values where possible.)
3 ln
3x
ex
 

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12. –/7 points UFLCalc1 1.6.001.Tut. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/7
 
An object is traveling in one direction on a straight line so that its distance from some fixed point is given by the table.
time
(s) 		0 1 2 3
distance
(meters) 		0 5 25 75
Find the average speed of the object during the following time intervals.
(a)    [0, 1]
m/s

(b)    [0, 2]
m/s

(c)    [0, 3]
m/s

(d)    [1, 2]
m/s

(e)    [1, 3]
m/s

(f)    [2, 3]
m/s

If you had to guess the speed at t = 2 just on the basis of these, what would you guess?
m/s

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