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人気のある微分積分 >

limit as x approaches 0 of 7/x-7cot(x)

解

x \to 0 lim (\frac{7}{x} - 7 cot (x))

解

0

解答ステップ

x \to 0 lim (\frac{7}{x} - 7 cot (x))

簡素化

\frac{7}{x} - 7 cot (x) : \frac{7 - 7 x cot ( x )}{x}

= x \to 0 lim (\frac{7 - 7 x cot ( x )}{x})

ロピタルの定理を適用する

= x \to 0 lim (\frac{- 7 ( - x csc ^{2} ( x ) + cot ( x ) )}{1})

簡素化

= x \to 0 lim (- 7 (- x csc^{2} (x) + cot (x)))

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

= - 7 \cdot x \to 0 lim (- x csc^{2} (x) + cot (x))

サイン, コサインで表わす

= - 7 \cdot x \to 0 lim (- \frac{x}{sin ^{2} ( x )} + \frac{cos ( x )}{sin ( x )})

簡素化

- \frac{x}{sin ^{2} ( x )} + \frac{cos ( x )}{sin ( x )} : \frac{- x + cos ( x ) sin ( x )}{sin ^{2} ( x )}

= - 7 \cdot x \to 0 lim (\frac{- x + cos ( x ) sin ( x )}{sin ^{2} ( x )})

ロピタルの定理を適用する

= - 7 \cdot x \to 0 lim (\frac{- 1 + cos ( 2 x )}{sin ( 2 x )})

ロピタルの定理を適用する

= - 7 \cdot x \to 0 lim (\frac{- 2 sin ( 2 x )}{cos ( 2 x ) \cdot 2})

値を挿入する

x = 0

= - 7 \cdot \frac{- 2 sin ( 2 \cdot 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

簡素化

- 7 \cdot \frac{- 2 sin ( 2 \cdot 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : 0

= 0

グラフ

人気の例

derivative f(x)=(sqrt(x))/(7+x)

d er i v a t i v e f (x) = \frac{x}{7 + x}

f(x)=e^x-e^{-x}-2x

f (x) = e^{x} - e^{- x} - 2 x

limit as x approaches-1 of (ln(x))/x

x \to - 1 lim (\frac{ln ( x )}{x})

laplacetransform 5H

l a pl a ce t r an s f or m 5 H

derivative of 2x^{5/2}

\frac{d}{d x} (2 x^{\frac{5}{2}})