limit as x approaches-infinity of (-3x^3-4x^2+2)/(5x^3+4x^2-2x)

解答

x \to - \infty lim (\frac{- 3 x ^{3} - 4 x ^{2} + 2}{5 x ^{3} + 4 x ^{2} - 2 x})

- \frac{3}{5}

十进制

- 0.6

求解步骤

x \to - \infty lim (\frac{- 3 x ^{3} - 4 x ^{2} + 2}{5 x ^{3} + 4 x ^{2} - 2 x})

除以分母的最高次幂:

\frac{- 3 - \frac{4}{x} + \frac{2}{x ^{3}}}{5 + \frac{4}{x} - \frac{2}{x ^{2}}}

= x \to - \infty lim (\frac{- 3 - \frac{4}{x} + \frac{2}{x ^{3}}}{5 + \frac{4}{x} - \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

不定型除外

= \frac{lim _{x \to - \infty} ( - 3 - \frac{4}{x} + \frac{2}{x ^{3}} )}{lim _{x \to - \infty} ( 5 + \frac{4}{x} - \frac{2}{x ^{2}} )}

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

x \to - \infty lim (5 + \frac{4}{x} - \frac{2}{x ^{2}}) = 5

= \frac{- 3}{5}

化简

= - \frac{3}{5}

\frac{d}{d x} (e^{- x} (a cos (x) + b sin (x)))

x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

\int \frac{sin ( k t )}{a + cos ( k t )} d t

x \to 3 lim (3 x^{2} + 4 x - 1)