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Evaluate the following limit: $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + a\sin bx} \right)^{1/x}} \end{array}$

Answer:

Given limit,

$\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + a\sin bx} \right)^{1/x}} \end{array}$