MATH 105 Lecture 36: MATH 105 Lecture 36
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Some handy rules to memorize: lim sin / = 1 lim (cos -1)/ = 1. This limit is simple because there is only a 6 in the denominator that we can just factor out. We cannot factor the 6 out of the sine here so to do this problem we need to notice that the sine is the same as the denominator ( i. e. both "s). We thus multiply the numerator and the denominator by 6. We have at this point factored the 6 in the numerator out of the limit. Now we need to do a change of variables. Let = 6x and as x 0. Now doing the change of variables on this limit gives us: This is the final solution c) lim x /sin(7x) x 0. At first glance it looks like the function we"re taking the limit of here is upside down but we can in fact rewrite it as:
