Question

Evaluate the following limits:
`lim_(xrarr0)(sin2x+sin3x)/(2x+sin3x)`

Answer 1

Correct Answer - 1
`lim_(xto0)(sin2x+sin3x)/(2x+sin3x)=lim_(xto0){((sin2x)/(x)+(sin3x)/(x))/(2+(sin3x)/(x))}" "["dividing num. and denom. by x"]`
`=lim_(xto0)(2x(sin2x)/(2x)+3xx(sin3x)/(3x))/(2+3xx(sin2x)/(3x))`
`=(2xxlim_(xto0)(sin2x)/(2x)+3xxlim_(xto0)(sin3x)/(3x))/(2+3xxlim_(xto0)(sin3x)/(3x))=((2xx1+3xx1))/((2+3xx1))=5/5=1.`