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cestrela7 [59]
2 years ago
6

Im h--> 0 ((Sqrt 9+h)-3)/h

Mathematics
1 answer:
Svetradugi [14.3K]2 years ago
6 0
\lim_{h \to 0}  \frac{ \sqrt{9+h}-3}{h} = \frac{ \sqrt{9+0} -3}{0}= \frac{0}{0} \\  \lim_{h \to 0}  \frac{ \sqrt{9+h}-3}{h}* \frac{ \sqrt{9+h}+3 }{ \sqrt{9+h} +3}= \\ = \lim_{h \to 0}   \frac{9+h-9}{h( \sqrt{9+h} +3)}  = \\   \lim_{n \to 0} \frac{h}{h( \sqrt{9+h}+3) }= \\ = \frac{1}{ \sqrt{9} +3}= 
= 1/6
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