limit as x approaches infinity of ((25x+7)sqrt(5x^2+2))/(5x^2+2)

Lösung

x \to \infty lim (\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2})

55

Dezimale

11.18033 \dots

Schritte zur Lösung

x \to \infty lim (\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2})

Vereinfache

\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2} : \frac{25 x + 7}{5 x ^{2} + 2}

= x \to \infty lim (\frac{25 x + 7}{5 x ^{2} + 2})

Teile durch den größten gemeinsamen Potenznenner:

\frac{25 + \frac{7}{x}}{5 + \frac{2}{x ^{2}}}

= x \to \infty lim \frac{25 + \frac{7}{x}}{5 + \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} ( 25 + \frac{7}{x} )}{lim _{x \to \infty} ( 5 + \frac{2}{x ^{2}} )}

x \to \infty lim (25 + \frac{7}{x}) = 25

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

= \frac{25}{5}

Vereinfache

\frac{25}{5} : 55

= 55

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