limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1)

Lösung

x \to \infty lim (\frac{3 8 x ^{9} + x ^{6} + 2}{4 x ^{3} + x ^{2} - 1})

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

x \to \infty lim (\frac{3 8 x ^{9} + x ^{6} + 2}{4 x ^{3} + x ^{2} - 1})

Teile durch den größten gemeinsamen Potenznenner:

\frac{3 8 + \frac{1}{x ^{3}} + \frac{2}{x ^{9}}}{4 + \frac{1}{x} - \frac{1}{x ^{3}}}

= x \to \infty lim \frac{3 8 + \frac{1}{x ^{3}} + \frac{2}{x ^{9}}}{4 + \frac{1}{x} - \frac{1}{x ^{3}}}

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} ( 3 8 + \frac{1}{x ^{3}} + \frac{2}{x ^{9}} )}{lim _{x \to \infty} ( 4 + \frac{1}{x} - \frac{1}{x ^{3}} )}

x \to \infty lim (3 8 + \frac{1}{x ^{3}} + \frac{2}{x ^{9}}) = 2

x \to \infty lim (4 + \frac{1}{x} - \frac{1}{x ^{3}}) = 4

= \frac{2}{4}

Streiche die gemeinsamen Faktoren:

2

= \frac{1}{2}

\int cos (x) (6 + 4 sin^{2} (x)) d x

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

y^{^{'}} = y sin (2 x)

x \to \infty lim (x (arctan (x) - \frac{π}{2}))

d er i v a t i v e f (x) = (7 x^{6} + 8 x^{3})^{4}