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人気のある微分積分 >

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

解

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

解

- \frac{1}{2}

+1

十進法表記

- 0.5

解答ステップ

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})

1 - 1 + x y

の共役で乗じる

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

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

簡素化

\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})

値を挿入する

x = 0

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

簡素化

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

= - \frac{1}{2}

グラフ

人気の例

limit as x approaches 0 of+1/x

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

limit as x approaches 3 of (3-sqrt(12-x))/(x-3)

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

limit as θ approaches 0 of sin(θ)cot(2θ)

θ \to 0 lim (sin (θ) cot (2 θ))

limit as x approaches 0+of tan(9x)

x \to 0 + lim (tan (9 x))

limit as x approaches 1 of (9x^8)/(5x^4)

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