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Beliebt Rechnen >

limit as x approaches-infinity of (sqrt(2x^2+3))/(2x+3)

Lösung

x \to - \infty lim (\frac{2 x ^{2} + 3}{2 x + 3})

Lösung

- \frac{1}{2}

+1

Dezimale

- 0.70710 \dots

Schritte zur Lösung

x \to - \infty lim (\frac{2 x ^{2} + 3}{2 x + 3})

Teile durch den größten gemeinsamen Potenznenner:

\frac{- 2 + \frac{3}{x ^{2}}}{2 + \frac{3}{x}}

= x \to - \infty lim \frac{- 2 + \frac{3}{x ^{2}}}{2 + \frac{3}{x}}

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

= - x \to - \infty lim \frac{2 + \frac{3}{x ^{2}}}{2 + \frac{3}{x}}

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= - \frac{lim _{x \to - \infty} ( 2 + \frac{3}{x ^{2}} )}{lim _{x \to - \infty} ( 2 + \frac{3}{x} )}

x \to - \infty lim (2 + \frac{3}{x ^{2}}) = 2

x \to - \infty lim (2 + \frac{3}{x}) = 2

= - \frac{2}{2}

Vereinfache

- \frac{2}{2} : - \frac{1}{2}

= - \frac{1}{2}

Graph

Beliebte Beispiele

limit as x approaches-1 of 3

x \to - 1 lim (3)

derivative of (x^3+4e^{3x})

\frac{d}{d x} ((x^{3} + 4) e^{3 x})

integral of (ln(-2x))/(5x)

\int \frac{ln ( - 2 x )}{5 x} d x

fläche y=x^2-7,y=6x

a re a y = x^{2} - 7, y = 6 x

integral of (1+x^2)/(1+x^4)

\int \frac{1 + x ^{2}}{1 + x ^{4}} d x