limit as t approaches 2-of-(3t)/(t-2)

解答

t \to 2 - lim (- \frac{3 t}{t - 2})

\infty

求解步骤

t \to 2 - lim (- \frac{3 t}{t - 2})

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

= - 3 \cdot t \to 2 - lim (\frac{t}{t - 2})

除以分母的最高次幂:

\frac{1}{1 - \frac{2}{t}}

= - 3 \cdot t \to 2 - lim (\frac{1}{1 - \frac{2}{t}})

t

从左侧趋近于

2, t < 2 \Rightarrow 1 - \frac{2}{t} < 0

分母从左侧趋近于 0，为负值

= - 3 (- \infty)

运用无穷大属性:

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

= \infty

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