limit as x approaches 9-of (5x)/(x-9)

解答

x \to 9 - lim (\frac{5 x}{x - 9})

- \infty

求解步骤

x \to 9 - lim (\frac{5 x}{x - 9})

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

= 5 \cdot x \to 9 - lim (\frac{x}{x - 9})

除以分母的最高次幂:

\frac{1}{1 - \frac{9}{x}}

= 5 \cdot x \to 9 - lim (\frac{1}{1 - \frac{9}{x}})

x

从左侧趋近于

9, x < 9 \Rightarrow 1 - \frac{9}{x} < 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

\frac{d}{d x} (- 4 x^{4} + 8 x^{3})

in v erse l a pl a ce \frac{( 3 s + 1 )}{s ( s + 2 )}

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{5} )}{x ^{18}}, y (1) = 1

d er i v a t i v e g (x) = 3 (5 - 7 x)^{5}

\frac{d}{d x} (sin (\frac{π}{4}))