Limits flashcards

16 practice cards drawn from the Limits lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

Read the Limits lessons in full →

What does 2 + 1/n as n grows without bound approach?

2

from “The Idea of a Limit”

What does 1/2 + 1/4 + 1/8 + … continuing forever approach?

1

from “The Idea of a Limit”

The left limit is 0 and the right limit is 0. Does the limit exist?

yes

from “One Sided Limits”

The left limit is 3 and the right limit is 3. Does the limit exist?

yes

from “One Sided Limits”

f → 8 and g → 0. May the quotient law be used on f / g?

no — the denominator’s limit is 0

from “The Limit Laws”

If f → 3 and g → 6, what does f × g approach?

18

from “The Limit Laws”

What is the limit of (x² − 9) / (x − 3) as x → 3?

6

from “Indeterminate Forms”

What is the limit of (x² − 16) / (x − 4) as x → 4?

8

from “Indeterminate Forms”

What is the limit of (2x + 3) / (3x + 5) as x → ∞?

2/3

from “Limits at Infinity”

What is the limit of (9x + 3) / (8x + 5) as x → ∞?

9/8

from “Limits at Infinity”

f is trapped between two functions that both approach 4. What does f approach?

4

from “The Squeeze Theorem”

f is trapped between two functions that both approach 2. What does f approach?

2

from “The Squeeze Theorem”

The squeeze proof traps sin x / x between which two functions?

cos x and 1

from “The Limit of sin x over x”

Why must x be in radians?

only in radians is sin x close to x near 0

from “The Limit of sin x over x”

For small x, cos x ≈ ?

1 − x²/2

from “Small-Angle Approximations”

The approximations hold only when x is measured in which unit?

radians

from “Small-Angle Approximations”

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