limit as x approaches 3+of (x+9)/(x-3)

解答

x \to 3 + lim (\frac{x + 9}{x - 3})

\infty

求解步骤

x \to 3 + lim (\frac{x + 9}{x - 3})

\frac{x + 9}{x - 3} = (x + 9) \frac{1}{x - 3}

= x \to 3 + lim ((x + 9) \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 (x + 9) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (x + 9) = 12

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

= 12 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

\frac{d}{d x} (\frac{2 x ^{2} + 4 x}{2 + x ^{2}})

f (x) = ln (3 x + 2)

d er i v a t i v e \frac{24}{x ^{2} + 12}

d er i v a t i v e x 3600 - x^{2}

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{2})