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Q. $\lim_{h \to0} \left(\frac{1}{h\sqrt[3]{8+h}} - \frac{1}{2h}\right) $ equals to

Limits and Derivatives

Solution:

$Lim_{h \to0} \frac{2-\sqrt[3]{8+h}}{2h.\sqrt[3]{8+h}}$
$ Lim_{h \to0} \frac{8-\left(8+h\right)}{2h.\sqrt[3]{8+h} \left\{8^{2/3} +8^{1/3} .\left(8+h\right)^{1/3} +\left(8+h\right)^{2/3}\right\}} = - \frac{1}{48} $