Question

Evaluate : \( \lim _{x \rightarrow \infty} x\{\ln (x+a)-\ln x\} \)

Comments

Please answer as soon as possible

Answer 1

lim_x->∞ x{ln(x+a)/x}

lim_x->∞ x{ln(1+a/x}

Let x=1/h

lim_x->∞ 1/h{ln(1+ah)}

Multiplying and Dividing by a

lim_x->∞ [ln(1+ah)]a/ah

Therefore 1×a=a  [ Since {ln(1+ah)/ah}=1]

Therefore, lim_x->∞ x{ln(x+a)/x}=a