limit as x approaches-2+of (5x)/(2+x)

解答

x \to - 2 + lim (\frac{5 x}{2 + x})

- \infty

求解步骤

x \to - 2 + lim (\frac{5 x}{2 + x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 5 \cdot x \to - 2 + lim (\frac{x}{2 + x})

除以分母的最高次幂:

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

= 5 \cdot x \to - 2 + lim (\frac{1}{\frac{2}{x} + 1})

x

从右侧趋近于

- 2, x > - 2 \Rightarrow \frac{2}{x} + 1 < 0

分母从左侧趋近于 0，为负值

= 5 (- \infty)

运用无穷大属性:

c \cdot (- \infty) = - \infty

= - \infty

f (x) = \frac{1}{20} sin (5 x^{2}) - \frac{1}{4} sin (x^{2})

t an g e n t f (x) = 3 x^{2} + 2 x - 5, (2, 7)

\int 15 e^{- 31 t} t d t

\frac{d}{d x} (3 y \cdot 4 x^{3})

d er i v a t i v e \frac{e ^{x} - 4}{ln ∣ x ∣}