When the limit x approaches 0, 1- cos x/2x^2, what is the limit?

Question

Hello everyone, any help or respones would be much appreciated please. :D

***The instructions is to evaluate the following limits using analytic techniques.

Answer 1

As x approaches 0, cos x approaches 1, right? And 2x^2 approaches 0. But the latter is in the denominator, and as the denominator approaches 0, the whole fraction approaches infinity.

It isn't clear from the way you wrote it if the denominator is only under cos x or is under 1 - cos x. In the latter case, as the denominator approaches 0, so does the numerator, which is a bit indeterminate. But in the former case, you have 1 minus infinity, which is negative infinity.

Answer 2

i think its 0. On a graph the y-values get closer and closer to 0 as the x's get closer to 0.