Limit of (ax - 1)/x
How to use the limit of Limit of (ax - 1)/x to solve the given limit with an exponential function: formula, 1 example, and its solution.
Formula
Example
Solution
Solution (Detail)
4x - 1
= 22x - 1
= (2x)2 - 12
Power of a Power
(2x)2 - 12 = (2x + 1)(2x - 1)
Factor the Difference of Two Squares: a2 - b2
Cancel the factors (2x + 1).
The exponent of 2x is x.
The denominator is also x.
So, as x → 0,
(2x - 1)/x → ln 2.
So ln 2 is the answer.