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.
