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AP Calculus AB: Chapter 12 Test

Mathematics15 CardsCreated 7 months ago

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

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Key Terms

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?
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

Related Flashcard Decks

TermDefinition

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

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.