Example Problem. L'Hopital's Rule

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:16px;font-family:ArialMT;color:#000000;} .ft02{font-size:16px;line-height:20px;font-family:ArialMT;color:#000000;} L'Hopital's Rule. Example Problem Let us consider the following example of L'Hopital's rule. If you evaluate the cosine of 0, you get 1. The exponential of 0 is 1, divided by 0 minus 0 – we get0/0. Factoring probably won't work, since there are no algebraic methods or anything that will help us.We'll use L'Hopital's rule instead. Thus, we take the derivative of the numerator (3sin3x), times 3 because of the chain rule, but youalready knew that. The derivative of e to the 4x is equal to 4 times e to the 4x divided by 2 times x minus 3. In otherwords, we can take the limit of each factor separately, then combine them when we have a limit onboth sides. So you plug in zero for the x-value. The sine of 0 is 0, minus e to the 0 is 1, times 4 is -4, dividedby 0 minus 3 is -3. So the limit would be 4/3. Here it is: L'Hopital's rule.