limit as x approaches infinity of (4x+2)/(2x-7)

解答

x \to \infty lim (\frac{4 x + 2}{2 x - 7})

2

求解步骤

x \to \infty lim (\frac{4 x + 2}{2 x - 7})

除以分母的最高次幂:

\frac{4 + \frac{2}{x}}{2 - \frac{7}{x}}

= x \to \infty lim (\frac{4 + \frac{2}{x}}{2 - \frac{7}{x}})

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} ( 4 + \frac{2}{x} )}{lim _{x \to \infty} ( 2 - \frac{7}{x} )}

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

x \to \infty lim (2 - \frac{7}{x}) = 2

= \frac{4}{2}

化简

= 2

y^{^{''}} - 6 y^{^{'}} + 18 y = 0

\int (3 x + 4)^{\frac{5}{2}} d x

d er i v a t i v e 1 + x

x \to 0 + lim (x^{2} e^{\frac{1}{x}})

\frac{d}{d x} (2 e^{- 2 x} + \frac{1}{3} e^{x})