1.

Evaluate the following limits: `lim_(xrarr0)(sinax+bx)/(ax+sinbx),where a, b, a+bne0`

Answer» Correct Answer - 1
`lim_(xto0)(sina+bc)/(ax+sin bx)=lim_(xto0){((sinax)/(x)+b)/(a+(sinbx)/(x))}" "["dividing num. and denom. by x"]`
`=lim_(xto0)({a((sinax)/(ax))+b})/({a+b((sinbx)/(bx))})=((axx1)+b)/(a+(bxx1))=(a+b)/(a+b)=1.`


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