Lim h - 0-x-h-x-h- y-0

Lim_h → 0√(x+h) √(x)/h, x ≠ 0 Rationalising the numerator =lim_h → 0(√(x+h) √(x))/h×(√(x+h)+√(x))/(√(x+h)+√(x)) =lim_h → 0(x+h x)/(√(x+h)+√(x))h =1/√(x)+√(x) =1 ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim h → 0√x+h...

Question

${lim}_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}, x \neq 0$

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Solution

${lim}_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}, x \neq 0$

Rationalising the numerator

$= {lim}_{h \to 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})}$

$= {lim}_{h \to 0} \frac{(x + h - x)}{(\sqrt{x + h} + \sqrt{x}) h}$

$= \frac{1}{\sqrt{x} + \sqrt{x}}$

$= \frac{1}{2 \sqrt{x}}$

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Similar questions

lim h \to 0 (\frac{\sqrt{x + h} - \sqrt{x}}{h})

Q. Evaluate

lim h \to 0 \frac{\sqrt{x + h} - \sqrt{x}}{h}

\lim_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}, x \neq 0

Q. Evaluate

lim h \to 0 \frac{\sqrt{(x + h)} - \sqrt{x}}{h}

which is

= \frac{1}{a \sqrt{(x)}}

Find

a

Find the value of $lim h \to 0 [2 - h] + lim h \to 0 [2 + h]$

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limh→0√x+h−√xh,x≠0

limh→0√x+h−√xh,x≠0 Rationalising the numerator =limh→0(√x+h−√x)h×(√x+h+√x)(√x+h+√x) =limh→0(x+h−x)(√x+h+√x)h =1√x+√x =12√x

${lim}_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}, x \neq 0$