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Evaluate : \( \lim _{x \rightarrow \infty} x\{\ln (x+a)-\ln x\} \) |
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Answer» limx->∞ x{ln(x+a)/x} limx->∞ x{ln(1+a/x} Let x=1/h limx->∞ 1/h{ln(1+ah)} Multiplying and Dividing by a limx->∞ [ln(1+ah)]a/ah Therefore 1×a=a [ Since {ln(1+ah)/ah}=1] Therefore, limx->∞ x{ln(x+a)/x}=a |
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