limit as x approaches infinity+of (x^5-3x^2+5x-9)/(7x^4-6x^2+5x-9)

Lösung

x \to \infty + lim (\frac{x ^{5} - 3 x ^{2} + 5 x - 9}{7 x ^{4} - 6 x ^{2} + 5 x - 9})

\infty

Schritte zur Lösung

x \to \infty lim (\frac{x ^{5} - 3 x ^{2} + 5 x - 9}{7 x ^{4} - 6 x ^{2} + 5 x - 9})

Teile durch den größten gemeinsamen Potenznenner:

\frac{x - \frac{3}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}}{7 - \frac{6}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}}

= x \to \infty lim (\frac{x - \frac{3}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}}{7 - \frac{6}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}})

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} ( x - \frac{3}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}} )}{lim _{x \to \infty} ( 7 - \frac{6}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}} )}

x \to \infty lim (x - \frac{3}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}) = \infty

x \to \infty lim (7 - \frac{6}{x ^{2}} + \frac{5}{x ^{3}} - \frac{9}{x ^{4}}) = 7

= \frac{\infty}{7}

Wende die Unendlichkeitseigenschaft an:

\frac{\infty}{c} = \infty

= \infty

\frac{d}{d x} (e^{l n (3)})

d er i v a t i v e y = x^{2} - 3 x + 3

\int \frac{1}{2 - 3 x - 4 x ^{2}} d x

f (x) = e^{2 x} - e^{- 2 x}

f^{^{'}} (x) = 4 sin^{2} (x)