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

解答

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

\infty

求解步骤

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

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

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

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

x \to 1 + lim (x^{2} + 1) = 2

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

= 2 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

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