limx→∞exx

The limit of the function e^x/x as x approaches infinity is infinity. Here's why:

Step 1: Recognize the form of the limit. As x approaches infinity, both e^x and x are also approaching infinity. This is an indeterminate form of type ∞/∞.

Step 2: Apply L'Hopital's Rule. This rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives. So, we differentiate the numerator and the denominator:

The derivative of e^x is e^x. The derivative of x is 1.

So, the limit becomes: lim (e^x/1) as x approaches infinity.

Step 3: Evaluate the limit. As x approaches infinity, e^x also approaches infinity. So, the limit is infinity.

Therefore, lim (e^x/x) as x approaches infinity is infinity.