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Beliebt Rechnen >

limit as n approaches infinity of sqrt(n^4+2n^3)-(n^2+n)

Lösung

n \to \infty lim (n^{4} + 2 n^{3} - (n^{2} + n))

Lösung

- \frac{1}{2}

+1

Dezimale

- 0.5

Schritte zur Lösung

n \to \infty lim (n^{4} + 2 n^{3} - (n^{2} + n))

Multipliziere mit der Konjugation von

n^{4} + 2 n^{3} - (n^{2} + n) : \frac{- n ^{2}}{n ^{4} + 2 n ^{3} + ( n ^{2} + n )}

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Teile durch den größten gemeinsamen Potenznenner:

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

= - n \to \infty lim \frac{1}{1 + \frac{2}{n} + 1 + \frac{1}{n}}

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

n \to \infty lim (1) = 1

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

= - \frac{1}{2}

Graph

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\int_{0}^{1} (9 x^{e} + 2 e^{x}) d x

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limit as x approaches 2 of 5x-2

x \to 2 lim (5 x - 2)