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