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Beliebt Rechnen >

limit as x approaches 0+of 1/(x^2)+ln(x)

Lösung

x \to 0 + lim (\frac{1}{x ^{2}} + ln (x))

Lösung

\infty

Schritte zur Lösung

x \to 0 + lim (\frac{1}{x ^{2}} + ln (x))

Vereinfache

\frac{1}{x ^{2}} + ln (x) : \frac{1 + x ^{2} ln ( x )}{x ^{2}}

= x \to 0 + lim (\frac{1 + x ^{2} ln ( x )}{x ^{2}})

\frac{1 + x ^{2} ln ( x )}{x ^{2}} = (1 + x^{2} ln (x)) \frac{1}{x ^{2}}

= x \to 0 + lim ((1 + x^{2} ln (x)) \frac{1}{x ^{2}})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= x \to 0 + lim (1 + x^{2} ln (x)) \cdot x \to 0 + lim (\frac{1}{x ^{2}})

x \to 0 + lim (1 + x^{2} ln (x)) = 1

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

Graph

Beliebte Beispiele

integral of (-10)/(x^2(25-x^2)^{1/2)}

\int \frac{- 10}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} d x

tangent sqrt(x)(x-8)

t an g e n t x (x - 8)

integral of \sqrt[4]{x}

\int 4 x d x

limit as x approaches 4 of (x^4-256)/(x^3-64)

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

maclaurin (1+x^2)^{-3/2}

ma c l a u r in (1 + x^{2})^{- \frac{3}{2}}