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?

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- Jan 18th 2008, 05:44 AMHockey_Guy14Need 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? - Jan 18th 2008, 05:52 AMPlato
Factor #1.

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

$ - Jan 18th 2008, 05:58 AMKrizalid
$\displaystyle \lim_{x \to 0} \frac{{(x + 8)^{1/3} - 2}}

{x}.$

Substitute $\displaystyle u^3=x+8,$

$\displaystyle \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.

Yes