Question

Show that lim g(x)=f'(x), f'(x) = -1/x^2, g(x) = (1/(x+h)-1/x)/h

Answer 1

did u try this ?where r u stuck ?

Answer 2

Umm I'm not really sure where to begin.

Answer 3

ok, so u need to find
\(\large \lim \limits_{x \rightarrow 0} \dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h}\)
right ?

Answer 4

can u solve numerator part ?

Answer 5

yes. to show that it is equal to \[\frac{ -1 }{x ^{2} }\]

Answer 6

1/x-1/x=0?

so h/h, which = 1?

Answer 7

sorry, it should be
\(\large \lim \limits_{h \rightarrow 0} \dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h}\)
and no, how u got that ?