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Questions and Answers
When evaluating the limit of sin t / t as t approaches 0, what is the most correct result?
When evaluating the limit of sin t / t as t approaches 0, what is the most correct result?
- The limit is undefined
- The limit is 1 (correct)
- The limit is 0
- The limit is approaching infinity
What is the correct evaluation of the limit of 1 - cos t / t as t approaches 0?
What is the correct evaluation of the limit of 1 - cos t / t as t approaches 0?
- The limit is approaching 1 (correct)
- The limit is 0
- The limit is approaching infinity
- The limit is undefined
When evaluating the limit of e^t - 1 / t as t approaches 0, what is the most accurate result?
When evaluating the limit of e^t - 1 / t as t approaches 0, what is the most accurate result?
- The limit is approaching e
- The limit is approaching infinity
- The limit is 1 (correct)
- The limit is undefined
What is the best evaluation of the given expression sin t / t for very large values of t?
What is the best evaluation of the given expression sin t / t for very large values of t?
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Study Notes
Evaluating Limits of Trigonometric and Exponential Functions
- As t approaches 0, the limit of sin t / t is 1.
- The limit of 1 - cos t / t as t approaches 0 is 0.
- The limit of e^t - 1 / t as t approaches 0 is 1.
- For very large values of t, the expression sin t / t approaches 0, because the amplitude of sin t is bounded between -1 and 1, while t grows indefinitely.
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