Write the value of lim x - 0sin x -1- x -1

Lim_x → 0sin x /√(1+ x 1) = lim_x → 0sin x/√(1 + x 1)×(f√(1 +x) +1 )/(√(1 + x ) + 1 ) = lim_x → 0sin x (√(1 + x)+ 1 )/1 + x 1 = lim_x → 0sin x /x(√(1 + ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

Write the val...

Question

Write the value of ${lim}_{x \to 0} \frac{s i n x}{\sqrt{1 + x - 1}} .$

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Solution

${lim}_{x \to 0} \frac{s i n x}{\sqrt{1 + x - 1}} = {lim}_{x \to 0} \frac{sin x}{\sqrt{1 + x - 1}} \times \frac{(f \sqrt{1 + x} + 1)}{(\sqrt{1 + x} + 1)} = {lim}_{x \to 0} \frac{sin x (\sqrt{1 + x} + 1)}{1 + x - 1} = {lim}_{x \to 0} \frac{sin x}{x} (\sqrt{1 + x} + 1) = \sqrt{1} + 1 = {lim}_{x \to 0} \frac{sin x}{\sqrt{1 + x - 1}} = 2$

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Write the value of limx→0sinx√1+x−1.

limx→0sinx√1+x−1=limx→0sinx√1+x−1×(f√1+x+1)(√1+x+1)=limx→0sinx(√1+x+1)1+x−1=limx→0sinxx(√1+x+1)=√1+1=limx→0sinx√1+x−1=2

Write the value of ${lim}_{x \to 0} \frac{s i n x}{\sqrt{1 + x - 1}} .$