What is the limit as h approaches+0 of (1/(a+h)-1/a)/h ?

The limit as h approaches+0 of (1/(a+h)-1/a)/h is -1/(a^2)

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limit as h approaches+0 of (1/(a+h)-1/a)/h

h \to + 0 lim (\frac{\frac{1}{a + h} - \frac{1}{a}}{h})

- \frac{1}{a ^{2}}

Solution steps

h \to 0 lim (\frac{\frac{1}{a + h} - \frac{1}{a}}{h})

Simplify

\frac{\frac{1}{a + h} - \frac{1}{a}}{h} : - \frac{1}{a ( h + a )}

= h \to 0 lim (- \frac{1}{a ( h + a )})

Plug in the value

h = 0

= - \frac{1}{a ( 0 + a )}

a (0 + a) = a^{2}

= - \frac{1}{a ^{2}}

\frac{d}{d t} (t)

\int t^{- 3} d t

\int \frac{x ^{3}}{25 + x ^{2}} d x

f (x) = - 3 x^{2} + 12, at x = 3

8 x^{2} y + y^{^{'}} = 10 x^{2}

What is the limit as h approaches+0 of (1/(a+h)-1/a)/h ?
The limit as h approaches+0 of (1/(a+h)-1/a)/h is -1/(a^2)