Suppost thatfis a differentiable function such that $\displaystyle f'(8)=2$. Without using L'Hospital's Rule, find the value of $\displaystyle \displaystyle\lim_{x\to 8}\frac{f(x)-f(8)}{x^{\frac{1}{3}}-2}$

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- Nov 5th 2007, 12:33 PMpolymeraseDifferent kind of Limit Problem
Suppost that

*f*is a differentiable function such that $\displaystyle f'(8)=2$. Without using L'Hospital's Rule, find the value of $\displaystyle \displaystyle\lim_{x\to 8}\frac{f(x)-f(8)}{x^{\frac{1}{3}}-2}$ - Nov 5th 2007, 12:46 PMJhevon
- Nov 5th 2007, 12:50 PMpolymerase
- Nov 5th 2007, 01:01 PMJhevon
do you not see the limit we want in there?

$\displaystyle 2 = \lim_{x \to 8} \frac {f(x) - f(8)}{\left( x^{\frac 13} - 2 \right) \left( x^{\frac 23} + 2x^{\frac 13} + 4 \right) } = \lim_{x \to 8} \frac {f(x) - f(8)}{x^{\frac 13} - 2} \cdot \frac 1{x^{\frac 23} + 2x^{\frac 13} + 4}$

what about now? - Nov 5th 2007, 01:15 PMpolymerase
- Nov 5th 2007, 01:20 PMJhevon
- Nov 5th 2007, 01:24 PMpolymerase