Evaluate limh- 0- x-h -x-h which is -1-a- x Find a

Required limit is, =lim_h→ 0√( ( x+h )) √(x)/h =lim_h→ 0√( ( x+h )) √(x)/h.√( ( x+h ))+√(x)/√( ( x+h ))+√(x) = lim_h→ 0 ( x+h ) x/h nbsp; ...

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Question

Evaluate $lim h \to 0 \frac{\sqrt{(x + h)} - \sqrt{x}}{h}$ which is $= \frac{1}{a \sqrt{(x)}}$ Find $a$

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

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

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

f (x)

x = a

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

f

lim h \to 0 \frac{f (- x) - f (- x - h)}{h} = lim h \to 0 \frac{f (x) - f (x - h)}{- h}

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