Question
ch8 Evaluate the limitlim x e x x k , where k is a positive constant. Additional Materials eBook 2. [-/1 Points] DETAILS OSCALC1 4.8.358.
ch8
Evaluate the limitlim
x
ex
xk
,
wherekis a positive constant.
Additional Materials
- eBook
2.
[-/1 Points]
DETAILS
OSCALC1 4.8.358.
MY NOTES
ASK YOUR TEACHER
Evaluate the limitlim
x
ln(x)
xk
,
wherekis a positive constant.
Additional Materials
- eBook
3.
[-/1 Points]
DETAILS
OSCALC1 4.8.361.
MY NOTES
ASK YOUR TEACHER
Evaluate the limitlim
xa
xa
xnan
,
wherenandaare constants.
Additional Materials
- eBook
4.
[-/3 Points]
DETAILS
OSCALC1 4.8.362.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following limit.
lim
x0+
x4ln(x)
Determine whether you can apply L'Hpital's rule directly. Explain why or why not.
L'Hpital's rule
---Select---
can
cannot
be applied directly because the limit is of the following form.
0
0
1
0
00
0
none of the above
How can the limit be altered in order to apply L'Hpital's rule? (Select all that apply.)
The limit can be rewritten using algebraic manipulation.
The limit can be rewritten by taking the logarithm of the limit and using properties of logarithms.
The limit cannot be rewritten in a form where L'Hpital's rule can be applied.
The limit does not need to be rewritten since L'Hpital's rule can be applied directly.
Additional Materials
- eBook
5.
[-/3 Points]
DETAILS
OSCALC1 4.8.364.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following limit.
lim
x0
x2x
Determine whether you can apply L'Hpital's rule directly. Explain why or why not.
L'Hpital's rule
---Select---
can
cannot
be applied directly because the limit is of the following form.
0
0
1
0
00
0
none of the above
How can the limit be altered in order to apply L'Hpital's rule? (Select all that apply.)
The limit can be rewritten using algebraic manipulation.
The limit can be rewritten by taking the logarithm of the limit and using properties of logarithms.
The limit cannot be rewritten in a form where L'Hpital's rule can be applied.
The limit does not need to be rewritten since L'Hpital's rule can be applied directly.
Additional Materials
- eBook
6.
[-/3 Points]
DETAILS
OSCALC1 4.8.366.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following limit.
lim
x
ex
x2
Determine whether you can apply L'Hpital's rule directly. Explain why or why not.
L'Hpital's rule
---Select---
can
cannot
be applied directly because the limit is of the following form.
0
0
1
0
00
0
none of the above
How can the limit be altered in order to apply L'Hpital's rule? (Select all that apply.)
The limit can be rewritten using algebraic manipulation.
The limit can be rewritten by taking the logarithm of the limit and using properties of logarithms.
The limit cannot be rewritten in a form where L'Hpital's rule can be applied.
The limit does not need to be rewritten since L'Hpital's rule can be applied directly.
Additional Materials
- eBook
7.
[-/1 Points]
DETAILS
OSCALC1 4.8.367-395A.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
t
9tln(t)
6+t2
TutorialAdditional Materials
- eBook
8.
[-/1 Points]
DETAILS
OSCALC1 4.8.367-395B.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's Rule or previously learned methods.
lim
x0
2e4x2
sin(x)
TutorialAdditional Materials
- eBook
9.
[-/1 Points]
DETAILS
OSCALC1 4.8.367-395C.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's Rule or previously learned methods.
lim
x9
9
x+72
81x2
TutorialAdditional Materials
- eBook
10.
[-/1 Points]
DETAILS
OSCALC1 4.8.367-395E.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's Rule or previously learned methods.
lim
x0
6x+exe7x
1cos(8x)
TutorialAdditional Materials
- eBook
11.
[-/1 Points]
DETAILS
OSCALC1 4.8.370.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
x/2
cos(x)
2
x
Additional Materials
- eBook
12.
[-/1 Points]
DETAILS
OSCALC1 4.8.377.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
x0
exx1
5x2
Additional Materials
- eBook
13.
[-/1 Points]
DETAILS
OSCALC1 4.8.382.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
x0+
x7x
Additional Materials
- eBook
14.
[-/1 Points]
DETAILS
OSCALC1 4.8.385.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
x0+
xln(x3)
Additional Materials
- eBook
15.
[-/1 Points]
DETAILS
OSCALC1 4.8.387.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the limit with either L'Hpital's rule or previously learned methods.
lim
x
x9ex
Additional Materials
- eBook
16.
[-/1 Points]
DETAILS
OSCALC1 4.8.402.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Use a calculator to graph the function and estimate the value of the limit, then use L'Hpital's rule to find the limit directly.
lim
x0
2csc(x)2
x
Additional Materials
- eBook
17.
[-/1 Points]
DETAILS
OSCALC1 4.8.404.
MY NOTES
ASK YOUR TEACHER
Use a calculator to graph the function and estimate the value of the limit, then use L'Hpital's rule to find the limit directly.
lim
x0+
ln(x)
sin(x)
Computex1
andx2
using the specified iterative method.
xn+ 1=xn21
2
(a)
Start atx0=0.2.
x1
=x2
=
(b)
Start atx0=2.
x1
=x2
=
Additional Materials
- eBook
2.
[-/4 Points]
DETAILS
OSCALC1 4.9.416.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Computex1
andx2
using the specified iterative method. (Round your answers to four decimal places.)
xn+ 1=
xn
(a)
Start atx0=0.2.
x1
=x2
=
(b)
Start atx0=3.
x1
=x2
=
Additional Materials
- eBook
3.
[-/4 Points]
DETAILS
OSCALC1 4.9.418.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Computex1
andx2
using the specified iterative method.
xn+ 1= 3xn(1xn)
(a)
Start atx0=0.2.
x1
=x2
=
(b)
Start atx0=2.
x1
=x2
=
Use the specified method to attempt to solve the equation. If it does not work, explain why it does not work. (Select all that apply.)
Newton's method,x2+7= 0
Newton's method works and the zeros are7 and 7.
Newton's method works and the zeros are2.6458 and 2.6458.
There are no real solutions to the equation.
x1is always undefined.
Newton's method alternates back and forth between two values.
Additional Materials
- eBook
6.
[-/1 Points]
DETAILS
OSCALC1 4.9.449.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Use the specified method to attempt to solve the equation. If it does not work, explain why it does not work. (Select all that apply.)
solvingxn+ 1=xn3
starting atx0=1
This method works and the zero is 0.
This method works and the zero is 1
x1is always undefined.
This method alternates back and forth between two values.
There are no real solutions to the equation.
Find the antiderivative of the function. (UseCfor the constant of the antiderivative.)
f(x) =ex9x8+ sin(x)
Additional Materials
- eBook
2.
[-/1 Points]
DETAILS
OSCALC1 4.10.473.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the antiderivative of the function. (UseCfor the constant of the antiderivative.)
f(x) =x1 +4sin(2x)
Additional Materials
- eBook
3.
[-/1 Points]
DETAILS
OSCALC1 4.10.474-489A.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the general antiderivative for the function below; assume we have chosen an intervalIon which the function is continuous. The function may require an algebraic manipulation first. (UseCfor the constant of integration.)
f(x) =39
40x7/8
F(x) =
TutorialAdditional Materials
- eBook
4.
[-/1 Points]
DETAILS
OSCALC1 4.10.474-489B.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the general antiderivative for the function below; assume we have chosen an intervalIon which the function is continuous. The function may require an algebraic manipulation first. (UseCfor the constant of integration.)
f(x) =5sec2(x)
F(x) =
TutorialAdditional Materials
- eBook
5.
[-/1 Points]
DETAILS
OSCALC1 4.10.474-489C.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the general antiderivative for the function below; assume we have chosen an intervalIon which the function is continuous. The function may require an algebraic manipulation first. (UseCfor the constant of integration.)
f(x) =16sin(x) +4cos(4x)
F(x) =
TutorialAdditional Materials
- eBook
6.
[-/1 Points]
DETAILS
OSCALC1 4.10.474-489D.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the general antiderivative for the function below; assume we have chosen an intervalIon which the function is continuous. The function may require an algebraic manipulation first. (UseCfor the constant of integration. Remember to use absolute values where appropriate.)
f(x) =(6+
x
)2
x
F(x) =
TutorialAdditional Materials
- eBook
7.
[-/1 Points]
DETAILS
OSCALC1 4.10.474-489E.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the general antiderivative for the function below; assume we have chosen an intervalIon which the function is continuous. The function may require an algebraic manipulation first. (UseCfor the constant of integration.)
f(x) =36x
6
x
F(x) =
TutorialAdditional Materials
- eBook
8.
[-/1 Points]
DETAILS
OSCALC1 4.10.475.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the antiderivativeF(x)
of the functionf(x).
(UseCfor the constant of the antiderivative.)
f(x) =x+27x2
F(x) =
Additional Materials
- eBook
9.
[-/1 Points]
DETAILS
OSCALC1 4.10.477.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the antiderivativeF(x)
of the functionf(x).
(UseCfor the constant of the antiderivative.)
f(x) = (
x
)5
F(x) =
Additional Materials
- eBook
10.
[-/1 Points]
DETAILS
OSCALC1 4.10.479.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the antiderivativeF(x)
of the functionf(x).
(UseCfor the constant of the antiderivative.)
f(x) =x1/3
x2/3
F(x) =
Additional Materials
- eBook
11.
[-/1 Points]
DETAILS
OSCALC1 4.10.484.
MY NOTES
ASK YOUR TEACHER
Find the antiderivativeF(x)
of the functionf(x).
(UseCfor the constant of the antiderivative.)
f(x) = 0
F(x) =
Additional Materials
- eBook
12.
[-/1 Points]
DETAILS
OSCALC1 4.10.490-498A.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the indefinite integral. (UseCfor the constant of integration.)
x6+
x
2dx
F(x) =
TutorialAdditional Materials
- eBook
13.
[-/1 Points]
DETAILS
OSCALC1 4.10.497.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the integral. (UseCfor the constant of integration.)
18x3+2x+1
x3
dx
Additional Materials
- eBook
14.
[-/1 Points]
DETAILS
OSCALC1 4.10.499-503.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the initial value problem.
dy
dx
=5x3,y(0) =8
y=
TutorialAdditional Materials
- eBook
15.
[-/1 Points]
DETAILS
OSCALC1 4.10.499.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the initial value problem.
f'(x) =x3,f(1) =7
f(x) =
Additional Materials
- eBook
16.
[-/1 Points]
DETAILS
OSCALC1 4.10.503.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the initial value problem.
f'(x) =4
x2
x2
4
,f(1) = 0
f(x) =
Additional Materials
- eBook
17.
[-/2 Points]
DETAILS
OSCALC1 4.10.902.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
First findf'(x)
and then findf(x).
f''(x) =x34x+8,f'(1) = 0,f(1) = 4
f'(x)=f(x)=
Tutorial
Analyze the graph off',
then list all intervals wherefis increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasingdecreasing
Additional Materials
- eBook
2.
[-/7 Points]
DETAILS
OSCALC1 4.5.228.
MY NOTES
ASK YOUR TEACHER
Consider the function. (If an answer does not exist, enter DNE.)
f(x) =x+x2x3
(a)
Determine intervals wherefis increasing or decreasing. (Enter your answers using interval notation.)
increasingdecreasing
(b)
Determine the local minima and maxima off. (Enter your answers as comma-separated lists.)
locations of local minimax=locations of local maximax=
(c)
Determine intervals wherefis concave up or concave down. (Enter your answers using interval notation.)
concave upconcave down
(d)
Determine the locations of inflection points off. (Enter your answers as a comma-separated list.)
x=
Additional Materials
- eBook
3.
[-/2 Points]
DETAILS
OSCALC1 4.6.280.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the horizontal and vertical asymptotes. (Letnrepresent an arbitrary integer. Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)
f(x) =6x+1
x1
horizontaly=verticalx=
TutorialAdditional Materials
- eBook
4.
[-/3 Points]
DETAILS
OSCALC1 4.6.902.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Write all horizontal and vertical asymptotes for the function; list any removable discontinuities (holes). (If an answer does not exist, enter DNE.)
f(x) =x22x
x24
vertical asymptotex=horizontal asymptotey=holex=TutorialAdditional Materials
- eBook
5.
[-/3 Points]
DETAILS
OSCALC1 4.7.316.WA.TUT.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
A rectangular box which is open at the top can be made from an12-by-30-inch piece of metal by cutting a square from each corner and bending up the sides. Find the dimensions of the box with greatest volume, whereh= height,l= length,andw= width.(Note:let the width be determined by the12-inch side and the length by the30-inch side.)h=inl=inw=inTutorialAdditional Materials
- eBook
6.
[-/2 Points]
DETAILS
OSCALC1 4.7.345.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Draw the given optimization problem and solve.
Find the dimensions (in units) of the closed cylinder with volumeV=54
units3that has the least amount of surface area.
radiusunitsheightunits
1..Find the change in volumedV(in units3) if the sides of a cube change from9to9.1.
dV=
units3
5.A woman wishes to rent a house within 9 miles of her work. If she livesxmiles from her work, her transportation cost will becxdollars per year, while her rent will be16c
x+ 1
dollars per year,
wherecis a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation? Use the methods outlined in this section to find the minimum.
x=mi
6.Determine over what interval(s) (if any) the Mean Value Theorem applies. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
y= ln(7x9)
7.Determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(t) =t+6
t2+7t+6
jump discontinuitiest=
n
removable discontinuitiest=infinite discontinuitiest=
other discontinuitiest=
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