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Evaluate lim(xtooo) (3^(sinx)+2x+1)/(sin...

Evaluate `lim_(xtooo) (3^(sinx)+2x+1)/(sinx-sqrt(x^(2))+1).`

Text Solution

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`underset(xtooo)lim(3^(sinx)+2x+1)/(sinx-sqrt(x^(2))+1)=underset(xtooo)lim((3^(sinx))/(x)+2+(1)/(x))/((sinx)/(x)-(1)/(x)sqrt(x^(2)+1))`
`=underset(xtooo)lim((3^(sinx))/(x)+2+(1)/(x))/((sinx)/(x)+(1)/(|x|)sqrt(x^(2)+1))`
`=underset(xtooo)lim((3^(sinx))/(x)+2+(1)/(x))/((sinx)/(x)+sqrt(1+(1)/(x^(2))))=2`
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