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

解答

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

\infty

求解步骤

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

除以分母的最高次幂:

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

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

x

从左侧趋近于

1, x < 1 \Rightarrow \frac{1}{x ^{2}} - 1 > 0

分母从右侧趋近于 0，为正值

= \infty

x \to 0 lim (sin (x) ln (\frac{1}{x}))

x \to 4 lim (\frac{x ^{2}}{21})

x \to a lim (2 x^{2} - 3 x + 2 a^{2})

x \to 1 + lim (ln (x - 1) + 3 x)

x \to 0 lim (4 x^{2} + 5 x - 6)