AP Calculus AB: Chapter 12 Test
This flashcard set covers fundamental limit problems in calculus, including indeterminate forms, applications of L'Hôpital’s Rule, and special trigonometric and exponential limits. It helps reinforce key concepts needed for solving standard limit problems in introductory calculus.
Evaluate lim x→0 tanx−x/sinx−x.
-2
Key Terms
Evaluate lim x→0 tanx−x/sinx−x.
-2
Evaluate lim x→∞ ln (lnx)/lnx
0
Evaluate lim x→0 √x+1/ln(x+1)
1/2
Evaluate lim x→0 1−cosx/x^2e^x
None of the above
True or false?
This limit meets the criteria for applying L′Hôpital’s rule
lim x→0 x/√3x^2+1
false
Evaluate lim x→π/2 (secx−tanx)
0
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| Term | Definition |
|---|---|
Evaluate lim x→0 tanx−x/sinx−x. | -2 |
Evaluate lim x→∞ ln (lnx)/lnx | 0 |
Evaluate lim x→0 √x+1/ln(x+1) | 1/2 |
Evaluate lim x→0 1−cosx/x^2e^x | None of the above |
True or false? | false |
Evaluate lim x→π/2 (secx−tanx) | 0 |
Evaluate lim x→∞ (1+5/x)^x. | e ^5 |
Evaluate lim x→∞ (x−√x^2+x) | −1/2 |
Evaluate lim x→∞ x sin(1/x). | 1 |
Evaluate lim x→0 (1/x−1/√x) | ∞ |
Evaluate the integral ∫2 0 dx/√2−x | 2√2 |
What is the value of ∫0 −1 dx/(x+1)^1/3 | 3/2 |
Evaluate ∫∞ 1 1/x^4 dx | 1/3 |
Evaluate ∫∞ 0 cosx dx. | The improper integral diverges |
Evaluate ∫π 0 2sec^2xdx | The integral diverges. |