limit as x approaches (0) of (1-sqrt(1+xy))/(xy)

解答

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

- \frac{1}{2}

十进制

- 0.5

求解步骤

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

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

= \frac{1}{y} \cdot x \to 0 lim (\frac{1 - 1 + x y}{x})

乘以

1 - 1 + x y

的共轭根式

: \frac{- x y}{1 + 1 + x y}

= \frac{1}{y} \cdot x \to 0 lim (\frac{\frac{- x y}{1 + 1 + x y}}{x})

化简

\frac{\frac{- x y}{1 + 1 + x y}}{x} : - \frac{y}{1 + x y + 1}

= \frac{1}{y} \cdot x \to 0 lim (- \frac{y}{1 + x y + 1})

代入值

x = 0

= \frac{1}{y} (- \frac{y}{1 + 0 \cdot y + 1})

化简

\frac{1}{y} (- \frac{y}{1 + 0 \cdot y + 1}) : - \frac{1}{2}

= - \frac{1}{2}

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

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

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x \to 1 lim (\frac{9 x ^{8}}{5 x ^{4}})