\Lim_{x\to0} {e^x-1}/\sqrt{1+x}-1} =

AP ICET 2019 Shift 1 Paper

Question : 134 of 200

Marks: +1, -0

\Lim↙{x→0} {e^x-1}/{√{1+x}-1}

Solution:

\lt↙{x → 0} \;{e^{x}-1}/{√{1+x}-1} ×{√{1+x}+1}/{√{1+x}+1}

=\lim ↙{x → 0} \;{e^{x}-1}/{x}[√{1+x}+1]

=2( ∵{\Lt}↙{x → 0} \;{e^{x}-1}/{x}=1)

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