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

Lösung

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

0

Schritte zur Lösung

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

Teile durch den größten gemeinsamen Potenznenner:

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

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

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

x \to \infty lim (\frac{5}{x} + \frac{7}{x ^{2}}) = 0

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

= \frac{0}{6}

Wende Regel an

\frac{0}{a} = 0, a \neq = 0

= 0