# Limit of (e^{x} - 1)/x

How to use the limit of Limit of (e^{x} - 1)/x to solve the given limit with an exponential function: formula, 1 example, and its solution.

## Formula

## Examplelim_{x → 0} (e^{6x} - 1)/x

Solution

Solution (Detail)

First write the limit part and (e^{6x} - 1).

The exponent of e^{6x} is 6x.

So write 6x

in the denominator.

The denominator of the given expression is x.

But you wrote 6x.

So, to undo the denominator 6,

multiply 6.

So (e^{6x} - 1)/x = [(e^{6x} - 1)/6x]⋅6.

As x → 0,

(e^{6x} - 1)/6x → 1

and write the constant 6.

1⋅6 = 6

So 6 is the answer.