# Need help evaluating limits

• January 18th 2008, 05:44 AM
Hockey_Guy14
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?
• January 18th 2008, 05:52 AM
Plato
Factor #1.
$\frac{{2^{x + 3} - 8}}{{2^x - 1}} = \frac{{2^3 \left( {2^x - 1} \right)}}{{2^x - 1}}

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• January 18th 2008, 05:58 AM
Krizalid
Quote:

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.

Quote:

Originally Posted by Hockey_Guy14
Any help?

Yes