Limit of (ex - 1)/x

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

Formula

Formula

The limit of (ex - 1)/x as x → 0 is
1.

Limit of (ax - 1)/x

Example

Example

Solution

First write the limit part and (e6x - 1).

The exponent of e6x 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 (e6x - 1)/x = [(e6x - 1)/6x]⋅6.

As x → 0,
(e6x - 1)/6x → 1
and write the constant 6.

1⋅6 = 6

So 6 is the answer.