Chapter 12 Practice Test

Question 1

Evaluate lim x→0 sin x/cos x −1.

Answer 1

The limit does not exist

Question 2

Evaluate limx→∞ ln(x^100)/x

Answer 2

0

Question 3

Evaluate limx→π ln(π−x+1)/sinx

Answer 3

1

Question 4

Evaluate lim x→1 lnx/x^2−1

Answer 4

1/2

Question 5

For which of the following values of c would we get lim x→0 ln(coscx)/2x^2=−1?

Answer 5

2

Question 6

Evaluate lim x→0 2xln(x^2)

Answer 6

0

Question 7

Evaluate lim x→∞ ^x√x

Answer 7

1

Question 8

Evaluate lim x→0 x^2cscx.

Answer 8

0

Question 9

Evaluate lim x→0 (cscx−1/x)

Answer 9

0

Question 10

Evaluate the following as true or false.

Say that lim x→∞f(x)=∞ and lim x→∞g(x)=0,but that lim x→∞f(x)⋅g(x)=L, where L is positive and finite. Then lim x→∞f(1x)⋅g(1x)=1L.

Answer 10

false

Question 11

Evaluate ∫1 −1 1/x^3 dx.

Answer 11

The integral diverges.

Question 12

Evaluate ∫ ∞ 0 2xdx/x^2+1.

Answer 12

The integral diverges.

Question 13

What is the value of ∫ ∞ 0 e^−x dx?

Answer 13

1

Question 14

Evaluate ∫ ∞ 1 e^√x / 2√x dx

Answer 14

The integral diverges.

Question 15

Evaluate the following as true or false.
∫ 3 0 dx/x−1=ln|x−1|∣∣
∣∣30=ln3−ln1=ln3

Answer 15

false