Question

limx-->0 (x+1) ^5 -1/x​

Answer 1

Solution :

$\bf \: \: \bull \: \: \: \: \: \: \lim_{x \to 0} { \bigg(x + 1 \bigg)}^{5} - \frac{1}{x}$

$\begin{array}{c|c} \implies \sf\lim_{x \to {0}^{ + } } { \bigg(x + 1 \bigg)}^{5} - \frac{1}{x} & \implies \sf\sf\lim_{x \to {0}^{ - } } { \bigg(x + 1 \bigg)}^{5} - \frac{1}{x} \\ \\ \\\implies \sf \lim_{x \to {0}^{ - } } { \bigg( {0}^{ + } + 1 \bigg)}^{5} + \frac{1}{ {0}^{ + } } & \implies\sf \lim_{x \to {0}^{ - } } { \bigg( {0}^{ - } + 1 \bigg)}^{5} + \frac{1}{ {0}^{ - } }\\ \\ \\ \implies \sf 1 + \infty & \implies \sf 1 - \infty \\ \\ \\ \implies \bf \: \infty & \implies \sf \bf - \infty \end{array} \\ \\ \\ \bf \therefore \: \: limit \: \: doesn't \: exist$