13.   Evaluate the following limits \lim_{x \rightarrow 0 } \frac{\sin ax }{bx }

Answers (1)

The limit

\lim_{x \rightarrow 0 } \frac{\sin ax }{bx }

Here on directly putting the limits, the function becomes \frac{0}{0} form. so we try to make the function in the form of \frac{sinx}{x}. so,

\lim_{x \rightarrow 0 } \frac{\sin ax }{bx }

=\lim_{x \rightarrow 0 } \frac{\sin ax(ax) }{bx(ax) }

=\lim_{x \rightarrow 0 } \frac{\sin ax }{ax }\frac{a}{b}

As  \lim_{x\rightarrow 0}\frac{sinx}{x}=1

=1\cdot\frac{a}{b}

=\frac{a}{b}   (Answer)

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