Question 1:

(a) Complete the table below given f(x)=x+36x3.

Round your answers to four decimal places.

x	3.1	3.01	3.001	2.999	2.99	2.9
f(x)	____________	____________	____________	____________	____________	____________

(b) Estimate limx3(x+36x3).

Enter your answer to the nearest integer.

limx3(x+36x3)= ____________

Question 2:

Note: This problem has an example student explanation in the Feedback.

(a) Complete the table below given f(x)=sin(5x)x.

Round your answers to six decimal places.

x	0.1	0.01	0.001	0.001	0.01	0.1
f(x)	____________	____________	____________	____________	____________	____________

(b) Estimate limx0sin(5x)x.

Enter your answer to the nearest integer.

limx0sin(5x)x= ____________

Question 3:

Find limx-3(x2+9)1/3.

limx-3(x2+9)1/3= __________

Show your work and explain, in your own words, how you arrived at your answer. There are sample student explanations in the feedback to questions 2, 4, 6, and 8 that show the level of detail that is expected in your explanations.

__________

Question 4:

Note: This problem has an example student explanation in the Feedback.

Let F(x)={x2ex+4x<44x.

Thenlimx4F(x) = __________

Question 5:

Let F(x)={1(x3)3+2x<33x.

Findlimx3+F(x).

limx3+F(x)=__________

Question 6:

Note: This problem has an example student explanation in the Feedback.

Find limx-3|x+3|x+3.

limx-3|x+3|x+3. =__________

Question 7:

Evaluate the following limit.

Enter the exact answer.

To entera,type sqrt(a).

limx0x+77-x=

__________

Hint: You may want to rationalize this function by multiplying both the numerator and the denominator by x+7+7-.

Show your work and explain, in your own words, how you arrived at your answer. There are sample student explanations in the feedback to questions 2, 4, 6, and 8 that show the level of detail that is expected in your explanations.

__________

Question 8:

Note: This problem has an example student explanation in the Feedback.

Evaluate the following limit.

Enter an exact answer.

limx9x281x+9= ____________

Question 9:

Evaluate the following limit.

Enter the exact answer.

To entera,type sqrt(a).

limx1x+32x1=

__________

Hint: You may want to rationalize this function by multiplying both the numerator and the denominator by x+3+2.

Question 10:

Use the Squeeze Theorem to find limx2f(x), given that 3|x2|f(x)3+|x2|.

limx2f(x)= ____________