limit as x approaches infinity of (6x^2-7x+10)/(5x^3+2x^2-4x+5)

Lösung

x \to \infty lim (\frac{6 x ^{2} - 7 x + 10}{5 x ^{3} + 2 x ^{2} - 4 x + 5})

0

Schritte zur Lösung

x \to \infty lim (\frac{6 x ^{2} - 7 x + 10}{5 x ^{3} + 2 x ^{2} - 4 x + 5})

Teile durch den größten gemeinsamen Potenznenner:

\frac{\frac{6}{x} - \frac{7}{x ^{2}} + \frac{10}{x ^{3}}}{5 + \frac{2}{x} - \frac{4}{x ^{2}} + \frac{5}{x ^{3}}}

= x \to \infty lim (\frac{\frac{6}{x} - \frac{7}{x ^{2}} + \frac{10}{x ^{3}}}{5 + \frac{2}{x} - \frac{4}{x ^{2}} + \frac{5}{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} ( \frac{6}{x} - \frac{7}{x ^{2}} + \frac{10}{x ^{3}} )}{lim _{x \to \infty} ( 5 + \frac{2}{x} - \frac{4}{x ^{2}} + \frac{5}{x ^{3}} )}

x \to \infty lim (\frac{6}{x} - \frac{7}{x ^{2}} + \frac{10}{x ^{3}}) = 0

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

= \frac{0}{5}

Wende Regel an

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

= 0

x \to 0 lim (x^{2} lo g_{e} (x))

x \to 2 - lim (x (2))

x \to \infty lim (\frac{2 x}{7})

x \to - 8 lim (x)

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