limit as x approaches 7+of x/(x^2-49)

解答

x \to 7 + lim (\frac{x}{x ^{2} - 49})

\infty

求解步骤

x \to 7 + lim (\frac{x}{x ^{2} - 49})

\frac{x}{x ^{2} - 49} = x \frac{1}{x ^{2} - 49}

= x \to 7 + lim (x \frac{1}{x ^{2} - 49})

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 7 + lim (x) \cdot x \to 7 + lim (\frac{1}{x ^{2} - 49})

x \to 7 + lim (x) = 7

x \to 7 + lim (\frac{1}{x ^{2} - 49}) = \infty

= 7 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

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