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人気のある微分積分 >

limit as y approaches 0 of (ysin(y))/(11y^2)

解

y \to 0 lim (\frac{y sin ( y )}{11 y ^{2}})

解

\frac{1}{11}

+1

十進法表記

0.09090 \dots

解答ステップ

y \to 0 lim (\frac{y sin ( y )}{11 y ^{2}})

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

= \frac{1}{11} \cdot y \to 0 lim (\frac{y sin ( y )}{y ^{2}})

共通因数を約分する:

y

= \frac{1}{11} \cdot y \to 0 lim (\frac{sin ( y )}{y})

ロピタルの定理を適用する

= \frac{1}{11} \cdot y \to 0 lim (\frac{cos ( y )}{1})

値を挿入する

y = 0

= \frac{1}{11} \cdot \frac{cos ( 0 )}{1}

簡素化

\frac{1}{11} \cdot \frac{cos ( 0 )}{1} : \frac{1}{11}

= \frac{1}{11}

グラフ

人気の例

limit as x approaches 45 of sin(x)

x \to 45 lim (sin (x))

limit as x approaches infinity of 5^x-1

x \to \infty lim (5^{x} - 1)

limit as x approaches 6 of (x-3)/(x+8)

x \to 6 lim (\frac{x - 3}{x + 8})

limit as x approaches 0 of x^{tan(x^2)}

x \to 0 lim (x^{t a n (x^{2})})

limit as x approaches 0 of 1/x-1/(2x^2)

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