limit as x approaches 0+of (x+5)/x

解答

x \to 0 + lim (\frac{x + 5}{x})

\infty

求解步骤

x \to 0 + lim (\frac{x + 5}{x})

除以分母的最高次幂:

1 + \frac{5}{x}

= x \to 0 + lim (1 + \frac{5}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定型除外

= x \to 0 + lim (1) + x \to 0 + lim (\frac{5}{x})

x \to 0 + lim (1) = 1

x \to 0 + lim (\frac{5}{x}) = \infty

= 1 + \infty

运用无穷大属性:

c + \infty = \infty

= \infty

x \to 5 lim (\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}})

x \to 4 + lim (\frac{2 x - 14}{x - 4})

x \to 7 lim (8 x)

x \to 0 + lim (tan (x) cot (x))

x \to 0 - lim (x^{5} + \frac{1}{x})