When is lhopitals rule applied

The derivative of our numerator is??? The derivative of our denominator is??? However, if plugging in??? How and when to use L'Hospital's rule. It does not directly evaluate limits, but only simplifies evaluation if used appropriately. No, it is not so clear why this would help, either, but we'll see in examples.

This problem illustrates the possibility as well as necessity of rearranging a limit to make it be a ratio of things, in order to legitimately apply L'Hospital's rule. But overall, the process is straightforward: if the limit is indeterminate, take the derivative of the top and the derivative of the bottom separately and then reevaluate the limit until you arrive at a defined value.

When I was studying calculus for the first time, this was the explanation given to me, and now I want to pass it along to you. Suppose we are taking the limit of a function as x approaches infinity and whose numerator and denominator subsequently approach infinity as well.

Is the numerator rapidly approaching infinity while the denominator is going to infinity more slowly? Or is the denominator speeding toward infinity, and the numerator is lagging behind? Click HERE to see a detailed solution to problem 4. Click HERE to see a detailed solution to problem 5. Click HERE to see a detailed solution to problem 6. Click HERE to see a detailed solution to problem 7.

Click HERE to see a detailed solution to problem 8.