limit as n approaches infinity of (nsqrt(n)-1)/(n^2+1)

Lösung

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

0

Schritte zur Lösung

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

Teile durch den größten gemeinsamen Potenznenner:

\frac{\frac{1}{n} - \frac{1}{n ^{2}}}{1 + \frac{1}{n ^{2}}}

= n \to \infty lim (\frac{\frac{1}{n} - \frac{1}{n ^{2}}}{1 + \frac{1}{n ^{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 _{n \to \infty} ( \frac{1}{n} - \frac{1}{n ^{2}} )}{lim _{n \to \infty} ( 1 + \frac{1}{n ^{2}} )}

n \to \infty lim (\frac{1}{n} - \frac{1}{n ^{2}}) = 0

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

= \frac{0}{1}

Wende Regel an

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

= 0

x \to 0 lim (x csc (x) sec (x))

x \to 0 lim ((2 + x)^{3} - 8 x)

x \to 2 lim ((x - 2)^{2} - 1)

x \to 0 lim (3 - 3 x + 6 x^{2})

x \to \infty lim ((\frac{1}{1 + \frac{5}{x}})^{x})