limit as x approaches 3+of (2x+1)/(x-3)

解答

x \to 3 + lim (\frac{2 x + 1}{x - 3})

\infty

求解步骤

x \to 3 + lim (\frac{2 x + 1}{x - 3})

\frac{2 x + 1}{x - 3} = (2 x + 1) \frac{1}{x - 3}

= x \to 3 + lim ((2 x + 1) \frac{1}{x - 3})

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

不定型除外

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

x \to 3 + lim (2 x + 1) = 7

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= 7 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

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