## Questions and Answers

What is the limit as x approaches 0 of sin(1/x)?

DNE

What is the limit as x approaches infinity of sin(1/x)?

0

What is the limit as x approaches 0 of sin(x)/x?

1

What is the limit as x approaches 0 of sin(ax)/ax?

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What is the limit as x approaches 0 of sin(ax)/bx?

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What is the limit as x approaches 0 of tan(x)/x?

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What is the limit as x approaches 0 of tan(ax)/ax?

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What is the limit as x approaches 0 of tan(ax)/bx?

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What is the limit as x approaches 0 of (1-cos(x))/x?

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What is the limit as x approaches 0 of (1-cos(ax))/ax?

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## Study Notes

### Special Limits

#### Sine Functions

- The limit as x approaches 0 of sin(1/x) does not exist (DNE)
- The limit as x approaches infinity of sin(1/x) is 0
- The limit as x approaches 0 of sin(x)/x is 1
- The limit as x approaches 0 of sin(ax)/ax is 1
- The limit as x approaches 0 of sin(ax)/bx is a/b

#### Tangent Functions

- The limit as x approaches 0 of tan(x)/x is 1
- The limit as x approaches 0 of tan(ax)/ax is 1
- The limit as x approaches 0 of tan(ax)/bx is a/b

#### Cosine Functions

- The limit as x approaches 0 of (1-cos(x))/x is 0
- The limit as x approaches 0 of (1-cos(ax))/ax is 0

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## Description

Flashcards covering special limits in calculus, including limits of trigonometric functions as x approaches 0 or infinity.