Question

$\underset{h\to 0}{lim}\left[\frac{1}{h\sqrt[3]{38+h}}-\frac{1}{2h}\right]$

Answer 1

$\underset{n\to 0}{lim}[\frac{1}{n\sqrt[2]{28+h}}-\frac{1}{2n}]$

$\underset{n\to 0}{lim}\left[\frac{2-\sqrt[2]{28+h}}{h\sqrt[3]{38+h}}\right]$

$\underset{n\to 0}{lim}\frac{(2-\sqrt[3]{38+h})(2{)}^2+(\sqrt[2]{28+h}{)}^2+2.\sqrt[3]{38+h}}{\left(h\sqrt[3]{38+h}\right)(2{)}^2+\sqrt[3]{38+h}+2\sqrt[3]{38+h}}$

$\underset{n\to 0}{lim}\frac{(2{)}^3-(8+h)}{n\sqrt[3]{38+h}(4+(\sqrt[3]{38+h}{)}^2+2\sqrt[3]{38+h})}$

$\underset{n\to 0}{lim}\frac{-1}{\left(\sqrt[3]{38+h}\right)(4+(\sqrt[3]{38+h}{)}^2+2\sqrt[3]{38+h})}$

$=\frac{-1}{2.(4+1+4)}$

$=\frac{-1}{24}$Ans