limit as x approaches-infinity of ((sqrt(5x^2-2)))/(x+3)

解答

x \to - \infty lim (\frac{( 5 x ^{2} - 2 )}{x + 3})

- 5

十进制

- 2.23606 \dots

求解步骤

x \to - \infty lim (\frac{5 x ^{2} - 2}{x + 3})

除以分母的最高次幂:

\frac{- 5 - \frac{2}{x ^{2}}}{1 + \frac{3}{x}}

= x \to - \infty lim \frac{- 5 - \frac{2}{x ^{2}}}{1 + \frac{3}{x}}

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to - \infty lim \frac{5 - \frac{2}{x ^{2}}}{1 + \frac{3}{x}}

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定型除外

= - \frac{lim _{x \to - \infty} ( 5 - \frac{2}{x ^{2}} )}{lim _{x \to - \infty} ( 1 + \frac{3}{x} )}

x \to - \infty lim (5 - \frac{2}{x ^{2}}) = 5

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

= - \frac{5}{1}

化简

= - 5

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})

x \to 3 lim (4 x^{3} - 5 x^{2} + x - 8)

\int sec^{2} (x) - csc (x) cot (x) d x

x \to - 3 lim (f (x) x)

y^{^{'}} = 8 y^{2} cos (t) + 7 y^{2} sin (4 t)