How do you evaluate the limit #(2-cos^2x)/x^2# as x approaches #0#?

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Answer 1 · 2018-03-12T15:35:22

#lim_(x->0) (2-cos^2x)/x^2 = +oo#

We know that:

#lim_(x->0) 1/x^2 = +oo#

And the numerator:

#2- cos^2x #

is bounded and positive because for any #x#:

#1 <= (2-cos^2x) <= 2#

Then:

#lim_(x->0) (2-cos^2x)/x^2 = +oo#

graph{(2-(cosx)^2)/x^2 [-10, 10, -5, 25]}