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Snowcat [4.5K]
3 years ago
13

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

Mathematics
1 answer:
motikmotik3 years ago
5 0
\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
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