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人気のある微分積分 >

limit as x approaches 0-of 1/x-csc(x)

解

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

解

0

解答ステップ

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

サイン, コサインで表わす

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

簡素化

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

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

ロピタルの定理を適用する

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

ロピタルの定理を適用する

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

値を挿入する

x = 0

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

簡素化

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

= 0

グラフ

人気の例

limit as θ approaches (3pi)/2 of sin(tan(cos(θ)))

θ \to \frac{3 π}{2} lim (sin (tan (cos (θ))))

limit as x approaches 2 of (4x-6)^4

x \to 2 lim ((4 x - 6)^{4})

limit as x approaches 3-of (x^2-9)/(x+3)

x \to 3 - lim (\frac{x ^{2} - 9}{x + 3})

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

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

limit as x approaches-4+of sqrt(16-x^2)

x \to - 4 + lim (16 - x^{2})