Mastering Limits: Evaluating (1-Cosx)/X Using L’Hopital’S Rule

limit as x approaches 0: 1-cosx/x

0

To evaluate the limit as x approaches 0 of (1-cosx)/x, we can use L’Hopital’s rule, which states that if we have an indeterminate form of 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator and then evaluate the limit again.

Applying L’Hopital’s rule, we take the derivative of the numerator and denominator separately:

(1 – cosx) / x = (sin x) / 1

Taking the limit as x approaches 0 of (sin x) / 1 yields sin 0 / 1 = 0/1 = 0.

Therefore, the limit as x approaches 0 of (1-cosx)/x is equal to 0.

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