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límite cuando x tiende a infinity de x/((ln(x))^3+2x)

Solución

x \to \infty lim (\frac{x}{( ln ( x ) ) ^{3} + 2 x})

\frac{1}{2}

Notación decimal

0.5

Pasos de solución

x \to \infty lim (\frac{x}{( ln ( x ) ) ^{3} + 2 x})

Aplicar la regla de L'Hopital

: x \to \infty lim (\frac{1}{\frac{3 l n ^{2} ( x )}{x} + 2})

= x \to \infty lim (\frac{1}{\frac{3 l n ^{2} ( x )}{x} + 2})

Simplificar

\frac{1}{\frac{3 l n ^{2} ( x )}{x} + 2} : \frac{x}{3 ln ^{2} ( x ) + 2 x}

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

Aplicar la regla de L'Hopital

: x \to \infty lim (\frac{1}{\frac{6 l n ( x )}{x} + 2})

= x \to \infty lim (\frac{1}{\frac{6 l n ( x )}{x} + 2})

Simplificar

\frac{1}{\frac{6 l n ( x )}{x} + 2} : \frac{x}{6 ln ( x ) + 2 x}

= x \to \infty lim (\frac{x}{6 ln ( x ) + 2 x})

Aplicar la regla de L'Hopital

: x \to \infty lim (\frac{1}{\frac{6}{x} + 2})

= x \to \infty lim (\frac{1}{\frac{6}{x} + 2})

Simplificar

\frac{1}{\frac{6}{x} + 2} : \frac{x}{6 + 2 x}

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

Dividir entre el denominador con mayor potencia:

\frac{1}{\frac{6}{x} + 2}

= x \to \infty lim (\frac{1}{\frac{6}{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

con excepción de forma indeterminada

= \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( \frac{6}{x} + 2 )}

x \to \infty lim (1) = 1

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

= \frac{1}{2}

2 y \frac{d y}{d x} = \frac{x}{x ^{2} - 16}, y (5) = 2

\int 9 x - 36 d x

\frac{d y}{d x} = 10 e^{x - y}

x^{^{''}} = x

x^{2} - 1 arcsec (x)