Lim_x→ 0√(1+x) √(1 x)/x lim_x→ 0(√(1+x) √(1 x))(√(1+x)+√(1 x))/x(√(1+x)+√(1 x)) =lim_x→ 01+x (1 x)/x(√(1+x)+√(1 x)) =lim_x→ 02x̸/x̸(√(1+x)+√(1 x)) =lim_x→ 02 ...

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Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

lim x → 01+x-...

Question

${lim}_{x \to 0} (1 + x - 1 - \frac{x}{x})$

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Solution

${lim}_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} {lim}_{x \to 0} \frac{(\sqrt{1 + x} - \sqrt{1 - x}) (\sqrt{1 + x} + \sqrt{1 - x})}{x (\sqrt{1 + x} + \sqrt{1 - x})} = {lim}_{x \to 0} \frac{1 + x - (1 - x)}{x (\sqrt{1 + x} + \sqrt{1 - x})} = {lim}_{x \to 0} \frac{2 / x}{/ x (\sqrt{1 + x} + \sqrt{1 - x})} = {lim}_{x \to 0} \frac{2}{\sqrt{1 + x} + \sqrt{1 - x}} = L$

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Similar questions

{lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{x} = {lim}_{x \to 0} \frac{(1 + x) \frac{1}{n} - 1}{(x + 1) - 1} =

lim x \to 0 {(\frac{1 + x}{1 - x})}^{1 / x}

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Q. Evaluate :

lim x \to 0 \frac{\frac{1}{x} + \frac{1}{2}}{x + 2}

lim x \to 0 \frac{{(1 + x)}^{n} - 1}{x}

\lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{2 x}

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limx→0(1+x−1−xx)

limx→0√1+x−√1−xxlimx→0(√1+x−√1−x)(√1+x+√1−x)x(√1+x+√1−x)=limx→01+x−(1−x)x(√1+x+√1−x)=limx→02/x/x(√1+x+√1−x)=limx→02√1+x+√1−x=L

${lim}_{x \to 0} (1 + x - 1 - \frac{x}{x})$