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受欢迎的微积分 >

limit as x approaches infinity of x/((ln(x))^3+2x)

解答

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

解答

\frac{1}{2}

+1

十进制

0.5

求解步骤

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

使用洛必达法则

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

化简

\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})

使用洛必达法则

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

化简

\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})

使用洛必达法则

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

化简

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

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

除以分母的最高次幂:

\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

不定型除外

= \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}

作图

流行的例子

2y(dy)/(dx)= x/(sqrt(x^2-16)),y(5)=2

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

(dy)/(dx)=10e^{x-y}

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

x^{^{''}} = x

(\partial)/(\partial y)(2e^yx)

\frac{\partial}{\partial y} (2 e^{y} x)

inverselaplace (3*s)/(5s^2+125)

in v erse l a pl a ce \frac{3 \cdot s}{5 s ^{2} + 125}