Question

Lim (h->0) (sqrt(25+h)-5)/h.

Answer 1

$\lim_{h \to 0} \frac{ \sqrt{25+h} -5}{h}= \frac{0}{0}$
We have to multiply numerator and denominator by: √(25-h)+ 5:
$\lim_{h \to 0} \frac{ \sqrt{25+h}-5}{h}* \frac{ \sqrt{25+h} +5}{ \sqrt{25+h}+5} = \\ \lim_{h \to 0} \frac{25+h-25}{h( \sqrt{25+h}+5) } = \\ \lim_{h \to 0} \frac{1}{ \sqrt{25+h} +5} = \\ = \frac{1}{5+5}=$= 1/10 = 0.1