MATH 105 Lecture Notes - Lecture 37: Trigonometric Functions
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While this limit may look intimidating, we can rewrite it as by splitting up the fraction. Now, we want a t in the denominator of the first and in the numerator of the second. We do this by multiplying the whole thing by t/t (which is just one after all and so won"t change the problem) and then do a little rearranging as follows: We can see that this is two limits that we"ve seen before. This limit almost looks the same in the sense that the sine is the same as what is in the denominator. However, notice that, in the limit, x is going to 4 and not 0 as the fact requires. However, with a change of variables we can see that this limit is in fact set to use the fact above regardless. So, let =x 4 and then notice that as x 4 we have 0.
