`lim_(t ->0) (cos(theta) - 1)/sin(theta)` Find the limit.

Textbook Question

Chapter 3, 3.3 - Problem 42 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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kspcr111 | In Training Educator

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`lim_(theta ->0) (cos(theta) - 1)/sin(theta)`

using L'Hopital's rule we get

so,

`lim_(theta ->0) ((cos(theta) - 1)')/(sin(theta)')`

`=lim_(theta ->0) (-sin(theta)/cos(theta))`

as `theta->0` we get

`= (-sin(0)/cos(0)) = 0`

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