Question

lim (1/a+h - 1/a) / h , a not equal to 0
h->0

pls answer ! :)

Answer 1

is it
\[\lim_{h \rightarrow 0 }\frac{ 1 }{ a+h }-\frac{ 1 }{ a }\]

Answer 2

it means same to find ferivative of f(a) = 1/a = a^-1
so, f'(a) = -a^(-1-1) = -a^-2 = -1/a^2

Answer 3

*derivative

Answer 4

but if u want using by limit method :
lim (h->0) (1/a+h - 1/a)/h
= lim (h->0) ((a-(a+h))/(a(a+h)h)
= lim (h->0) -h/(a(a+h)h)
= lim (h->0) -1/(a(a+h))
just plug h=0;
= -1/(a(a+0))
= -1/a*a
= -1/a^2

Answer 5

if u not sure, ask the god of math "wolfram"
http://www.wolframalpha.com/input/?i=lim+%28%281%2F%28a%2Bh%29%29+-+%281%2Fa%29%29%2Fh%2C+h%3D0%29