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人気のある微分積分 >

limit as x approaches 0 of (4sin(3x))/(2tan(5x))

解

x \to 0 lim (\frac{4 sin ( 3 x )}{2 tan ( 5 x )})

解

\frac{6}{5}

+1

十進法表記

1.2

解答ステップ

x \to 0 lim (\frac{4 sin ( 3 x )}{2 tan ( 5 x )})

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

= \frac{4}{2} \cdot x \to 0 lim (\frac{sin ( 3 x )}{tan ( 5 x )})

簡素化

= 2 \cdot x \to 0 lim (\frac{sin ( 3 x )}{tan ( 5 x )})

ロピタルの定理を適用する

= 2 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{sec ^{2} ( 5 x ) \cdot 5})

値を挿入する

x = 0

= 2 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 5 \cdot 0 ) \cdot 5}

簡素化

2 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 5 \cdot 0 ) \cdot 5} : \frac{6}{5}

= \frac{6}{5}

グラフ

人気の例

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

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

integral from 0 to 1 of (3x^2)/(1+x^3)

\int_{0}^{1} \frac{3 x ^{2}}{1 + x ^{3}} d x

x^2y^{''}-3xy^'+5y=0

x^{2} y^{^{''}} - 3 x y^{^{'}} + 5 y = 0

tangent f(x)=2x^2-9x+10,\at x=2

t an g e n t f (x) = 2 x^{2} - 9 x + 10, at x = 2

derivative of xarcsin(x)

\frac{d}{d x} (x arcsin (x))