How do you find the limit of $(1 - cos^2 1) / x$ as x approaches 0?

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Answer 1 · 2016-08-23T08:02:16

Limit does not exist

without typing numbers into a calculator!!

$lim_(x to 0) (1 - cos^2 1) / x$

$=lim_(x to 0) (sin^2 1) / x$

so the numerator is some positive number....

$=(sin^2 1) /(lim_(x to 0) x)$

But:
$(sin^2 1) /(lim_(x to 0^+) x) = oo$

whereas:
$(sin^2 1) /(lim_(x to 0^-) x) = -oo$

So the limit does not exist

How do you find the limit of (1 - cos^2 1) / x(1 - cos^2 1) / x as x approaches 0?