This means the limit of this algebraic fraction is indeterminate, and the limit doesn’t give us a clear picture of what is happening. Suppose we are taking the limit of a function as x approaches infinity and whose numerator and denominator subsequently approach infinity as well. 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. Okay, so without getting bogged down with semantics or the formal proof involving Cauchy’s Mean Value Theorem, let’s discuss why L’Hopital’s Rule works. Observe that we had to apply L’Hopital’s rule twice to find the limit value.īut 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.
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