Need help evaluating limits

**Hockey_Guy14** · January 18th 2008, 05:44 AM

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?

**Plato** · January 18th 2008, 05:52 AM

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

**Krizalid** · January 18th 2008, 05:58 AM

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

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