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人気のある微分積分 >

limit as x approaches 0+of 3(csc(x)-1/x)

解

x \to 0 + lim (3 (csc (x) - \frac{1}{x}))

解

0

解答ステップ

x \to 0 + lim (3 (csc (x) - \frac{1}{x}))

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

= 3 \cdot x \to 0 + lim (csc (x) - \frac{1}{x})

サイン, コサインで表わす

= 3 \cdot x \to 0 + lim (\frac{1}{sin ( x )} - \frac{1}{x})

簡素化

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

= 3 \cdot x \to 0 + lim (\frac{x - sin ( x )}{x sin ( x )})

ロピタルの定理を適用する

= 3 \cdot x \to 0 + lim (\frac{1 - cos ( x )}{sin ( x ) + x cos ( x )})

ロピタルの定理を適用する

= 3 \cdot x \to 0 + lim (\frac{sin ( x )}{2 cos ( x ) - x sin ( x )})

値を挿入する

x = 0

= 3 \cdot \frac{sin ( 0 )}{2 cos ( 0 ) - 0 \cdot sin ( 0 )}

簡素化

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

= 0

グラフ

人気の例

limit as x approaches infinity of 16

x \to \infty lim (16)

limit as x approaches 0 of 1^x

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

limit as z approaches 2i of z^2+3z

z \to 2 i lim (z^{2} + 3 z)

limit as x approaches e^2 of xln(x)

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

limit as h approaches 0 of 3/(h^2+2)

h \to 0 lim (\frac{3}{h ^{2} + 2})