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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Setze den Wert

h = 0

ein

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

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

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

Graph

Beliebte Beispiele

d/(dt)(sqrt(t))

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

integral of t^{-3}

\int t^{- 3} d t

integral of (x^3)/(sqrt(25+x^2))

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

tangent f(x)=-3x^2+12,\at x=3

t an g e n t f (x) = - 3 x^{2} + 12, at x = 3

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

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