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

解答

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

\infty

求解步骤

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

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

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

除以分母的最高次幂:

\frac{1}{1 - \frac{5}{x}}

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

x

从右侧趋近于

5, x > 5 \Rightarrow 1 - \frac{5}{x} > 0

分母从右侧趋近于 0，为正值

= 2 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

s im pl i f y 2 (\frac{2400}{x})

x (1 + y^{2}) d x = y (1 + x^{2}) d y

s l o p e (- 2, - 7), (3, 5)

y^{^{'}} = \frac{y}{x ^{2} + 1}

y^{^{''}} - 3 y^{^{'}} = x^{3} - 6