Find the limit of (cos(x)tan(x)) / x as x approaches 0?

Question

Find the limit of Cos(x)Tan(x) / x as x approaches 0 thanks for any help i've been working on this problem for 45 minutes and just end up with sin(x) / x

Answer 1

Lim ‘x’tending to ‘0’ costan/x=>cosx*(sinx/cosx)/x =>sinx/x =1
This is a standard limit

Answer 2

Hmm this is just a guess, but almost no matter what the value of the numerator is, the denominator is going to get very very small.
At first glance, I think it will be infinite. The question is, will the numerator approach 0 faster than the denominator.

So let's see...as x -> 0, cos(x) -> 1, tan(x) -> 0 is x and is always larger than x...but it keeps getting closer and closer to x....which means, cos is a wash, but since tan(x) gets closer and closer to x the smaller you get, I'm gonna guess that the limit of the equation is 1.

Hope that helps.

Answer 3

You are on the right track as it does indeed reduce to sin(x)/x If it helps just use a calculator and keep putting in smaller and smaller values of x like .01, .001, etc I believe that the answer is 1 as sin(x) is approximately x at small values of x so you get x/x or 1. Note that for this to work the x value in sin(x) is in radians, not degrees. If degrees then there is a multiplier.