\lim_{x\to0} ({{e^{5x}-e^{3x}}/{e^{4x}-e^x}) =

TS ICET 23 May 2019 Shift 2 Paper

Question : 134 of 200

Marks: +1, -0

\lim↙{x→0} ({{e^{5x}-e^{3x}}/{e^{4x}-e^x})

Solution:

\lim ↙{x → 0} \;{e^{5 x}-e^{3 x}}/{e^{4 x}-e^{x}}

{Lt}↙{x → 0} {\;{( e ^{5x}-1)}/{ x }-{( e ^{ x }-1)}/{ x }}/{({e^{4x}-1}/x-{e^{x}-1}/x)}={5-3}/{4-1}={2}/{3}

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