Is indeterminate form the only condition we need to check before using L’Hospital Rule?
Is the following limit evaluation correct?
lim x->0 (sin x / x)
= lim x->0 (cos x / 1) as sin x / x is in the form 0/0, (sin x)’ = cos x and x’ = 1
No, it is not correct.
The derivative of sin x is derived from the lim x->0 (sin x / x) = 1. We cannot use the L’Hospital Rule on lim x->x0 f(x)/g(x) if the derivative of either f(x) or g(x) is derived from the limit. The correct way to evaluate lim x->0 (sin x / x) is to use the Sandwich Theorem.
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