Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + a\sin bx} \right)^{1/x}} \end{array}$ ...
Exercise 29.11
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Evaluate the following limit: $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + \sin x} \right)^{1/x}}\\ \end{array}$
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + \sin x} \right)^{1/x}}\\ \end{array}$ f (x) = cos x + sin x – 1 g (x) =...
Evaluate the following limit: $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x} \right)^{1/\sin x}}\\ \end{array}$
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x} \right)^{1/\sin x}}\\ \end{array}$
Evaluate the following limit: $\begin{array}{l} \mathop {\lim }\limits_{x \to {0^ + }} {\left\{ {1 + {{\tan }^{\sqrt x }}} \right\}^{1/2x}}\\ \end{array}$
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to {0^ + }} {\left\{ {1 + {{\tan }^{\sqrt x }}} \right\}^{1/2x}}\\ \end{array}$
Evaluate the following limit: $\begin{array}{l} \mathop {\lim }\limits_{x \to \pi } {\left( {1 – \frac{x}{\pi }} \right)^2}\\ \end{array}$
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to \pi } {\left( {1 - \frac{x}{\pi }} \right)^2}\\ \end{array}$