Lim x - 0-1-x-1-log 1-x

Lim_x→ 0√(1+x) 1/log(1+x) =lim_x→ 0 (√(1+x) 1 ) (√(1+x)+1 )/log(1+x) (√(1+x)+1 ) =lim_x→ 0x/log(1+x) (√(1+x)+1 ) =lim_x→ 01/log(1+x)/x×lim_x→ 01/ ( √(1+ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 0√1+x...

Question

${lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{l o g (1 + x)}$

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Solution

${lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{l o g (1 + x)}$

$= {lim}_{x \to 0} \frac{(\sqrt{1 + x} - 1) (\sqrt{1 + x} + 1)}{l o g (1 + x) (\sqrt{1 + x} + 1)}$

$= {lim}_{x \to 0} \frac{x}{l o g (1 + x) (\sqrt{1 + x} + 1)}$

$= {lim}_{x \to 0} \frac{1}{\frac{l o g (1 + x)}{x}} \times {lim}_{x \to 0} \frac{1}{(\sqrt{1 + x} + 1)}$

$= 1 \times \frac{1}{2} = \frac{1}{2}$

Suggest Corrections

limx→0√1+x−1log(1+x)

limx→0√1+x−1log(1+x) =limx→0(√1+x−1)(√1+x+1)log(1+x)(√1+x+1) =limx→0xlog(1+x)(√1+x+1) =limx→01log(1+x)x×limx→01(√1+x+1) =1×12=12

${lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{l o g (1 + x)}$