# Math Help - Need help evaluating limits

1. ## Need help evaluating limits

Evaluate the following limits

Lim as x ->0 (2 to the power of x+3) subtract 8 divided by (2 to the power of x) subtract 1

lim as x ->0 (x + 8 to the power of 1/3) - 2 divided by x

Any help?

2. Factor #1.
$\frac{{2^{x + 3} - 8}}{{2^x - 1}} = \frac{{2^3 \left( {2^x - 1} \right)}}{{2^x - 1}}

$

3. Originally Posted by Hockey_Guy14
lim as x ->0 (x + 8 to the power of 1/3) - 2 divided by x
$\lim_{x \to 0} \frac{{(x + 8)^{1/3} - 2}}
{x}.$

Substitute $u^3=x+8,$

$\lim_{x \to 0} \frac{{(x + 8)^{1/3} - 2}}
{x} = \lim_{u \to 2} \frac{{u - 2}}
{{u^3 - 8}} = \lim_{u \to 2} \frac{1}
{{u^2 + 2u + 4}}.$

The rest follows.

Originally Posted by Hockey_Guy14
Any help?
Yes