Question

Find the limit of "e^x/x" as "x" approaches infinity.

Answer 1

To find the limit of e^x/x as x approaches infinity, we can use L'Hopital's Rule. Applying this rule, we find that the limit is infinity.

Step-by-step explanation:

To find the limit of “e^x/x” as “x” approaches infinity, we can use L'Hopital's Rule. This rule states that if the limit of f(x)/g(x) as x approaches a is of the form 0/0 or ∞/∞, then the limit is equal to the limit of f'(x)/g'(x) as x approaches a, provided this latter limit exists. Applying this rule to our limit:

1. Take the derivative of the numerator and denominator to get (e^x)/(1).
2. Now, take the limit as x approaches infinity. Since the derivative of e^x is e^x, the numerator approaches infinity, and the denominator approaches 1, so the limit is infinity.