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

해법

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

- \infty

솔루션 단계

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

\frac{x}{1 + x ^{3}} = x \frac{1}{1 + x ^{3}}

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

부정형을 제외하고

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

x \to - 1 + lim (x) = - 1

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

= (- 1) \cdot \infty

무한대 속성 적용:

- c \cdot \infty = - \infty

= - \infty