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人気のある微分積分 >

limit as x approaches 0 of 7(cot(x)-1/x)

解

x \to 0 lim (7 (cot (x) - \frac{1}{x}))

解

0

解答ステップ

x \to 0 lim (7 (cot (x) - \frac{1}{x}))

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

= 7 \cdot x \to 0 lim (cot (x) - \frac{1}{x})

サイン, コサインで表わす

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

簡素化

\frac{cos ( x )}{sin ( x )} - \frac{1}{x} : \frac{x cos ( x ) - sin ( x )}{x sin ( x )}

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

ロピタルの定理を適用する

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

ロピタルの定理を適用する

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

値を挿入する

x = 0

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

簡素化

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

= 0

グラフ

人気の例

limit as x approaches-4 of x^2-5x+3

x \to - 4 lim (x^{2} - 5 x + 3)

limit as x approaches 0 of 1/(x^n)

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

limit as x approaches 1/2 of x+3

x \to \frac{1}{2} lim (x + 3)

limit as x approaches 0 of e^2

x \to 0 lim (e^{2})

limit as x approaches 3+of x(3)

x \to 3 + lim (x (3))