limit as x approaches 4 of (4-sqrt(4+3x))/(4-x)

解答

x \to 4 lim (\frac{4 - 4 + 3 x}{4 - x})

\frac{3}{8}

十进制

0.375

求解步骤

x \to 4 lim (\frac{4 - 4 + 3 x}{4 - x})

乘以

4 - 4 + 3 x

的共轭根式

: \frac{- 3 x + 12}{4 + 4 + 3 x}

= x \to 4 lim (\frac{\frac{- 3 x + 12}{4 + 4 + 3 x}}{4 - x})

化简

\frac{\frac{- 3 x + 12}{4 + 4 + 3 x}}{4 - x} : \frac{3}{4 + 3 x + 4}

= x \to 4 lim (\frac{3}{4 + 3 x + 4})

代入值

x = 4

= \frac{3}{4 + 3 \cdot 4 + 4}

化简

\frac{3}{4 + 3 \cdot 4 + 4} : \frac{3}{8}

= \frac{3}{8}

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

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

x \to \frac{1}{8} lim (\frac{1}{x} + x - 1)

x \to 0 lim (\frac{( 2 + x )}{1 + x})

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