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  • Evaluate the following limits limit x tends to 0 ax + x cos x/ b sin x

18.   Evaluate the following limits \lim_{x \rightarrow 0}\frac{ax + x \cos x }{b \sin x }

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\lim_{x \rightarrow 0}\frac{ax + x \cos x }{b \sin x }

The function takes the form zero by zero when we put the limit directly in the function,. since function consist of sin function and cos function, we try to make the function in the form of \frac{sinx}{x} as we know that it tends to 1 when x tends to 0.

So,

\lim_{x \rightarrow 0}\frac{ax + x \cos x }{b \sin x }

=\frac{1}{b}\lim_{x \rightarrow 0}\frac{x(a+ \cos x) }{ \sin x }

=\frac{1}{b}\lim_{x \rightarrow 0}\frac{x }{ \sin x }\times(a+ \cos x)

=\frac{1}{b}\times1\times(a+ \cos (0))

=\frac{a+1}{b}   (Answer)

 

Posted by

Pankaj Sanodiya

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