AP Calculus AB: Chapter 12 Practice Test
This set of problems explores limits involving logarithmic and trigonometric functions, many of which result in indeterminate forms. Techniques used include direct substitution, algebraic simplification, L’Hôpital’s Rule, and known limit identities. Some limits evaluate to finite values, some approach zero, and others diverge or do not exist.
Evaluate lim x→0 sin x/cos x −1.
The limit does not exist
Key Terms
Evaluate lim x→0 sin x/cos x −1.
The limit does not exist
Evaluate limx→∞ ln(x^100)/x
0
Evaluate limx→π ln(π−x+1)/sinx
1
Evaluate lim x→1 lnx/x^2−1
1/2
For which of the following values of c would we get lim x→0 ln(coscx)/2x^2=−1?
2
Evaluate lim x→0 2xln(x^2)
0
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| Term | Definition |
|---|---|
Evaluate lim x→0 sin x/cos x −1. | The limit does not exist |
Evaluate limx→ ∞ ln(x^100)/x | 0 |
Evaluate limx→π ln(π−x+1)/sinx | 1 |
Evaluate lim x→1 lnx/x^2−1 | 1/2 |
For which of the following values of c would we get lim x→0 ln(coscx)/2x^2=−1? | 2 |
Evaluate lim x→0 2xln(x^2) | 0 |
Evaluate lim x→∞ ^x√x | 1 |
Evaluate lim x→0 x^2cscx. | 0 |
Evaluate lim x→0 (cscx−1/x) | 0 |
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. | false |
Evaluate ∫1 −1 1/x^3 dx. | The integral diverges. |
Evaluate ∫ ∞ 0 2xdx/x^2+1. | The integral diverges. |
What is the value of ∫ ∞ 0 e^−x dx? | 1 |
Evaluate ∫ ∞ 1 e^√x / 2√x dx | The integral diverges. |
Evaluate the following as true or false. | false |