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

20.   Evaluate the following limits \lim_{x\rightarrow 0} \frac{\sin ax + bx }{ax + \sin bx } a,b ,a + b \neq 0

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\lim_{x\rightarrow 0} \frac{\sin ax + bx }{ax + \sin bx } a,b ,a + b \neq 0

The function takes the zero by zero form when we put the limit into the function directly, so we try to eliminate this case by simplifying the function. So

\lim_{x\rightarrow 0} \frac{\sin ax + bx }{ax + \sin bx } a,b ,a + b \neq 0

=\lim_{x\rightarrow 0} \frac{\frac{\sin ax}{ax} \cdot ax+ bx }{ax + \frac{\sin bx}{bx}\cdot bx }

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

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

=\frac{a+b}{a+ b}

=1  (Answer)

Posted by

Pankaj Sanodiya

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