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人気のある微分積分 >

limit as x approaches infinity of ((10-6x^2))/(5+3e^x)

解

x \to \infty lim (\frac{( 10 - 6 x ^{2} )}{5 + 3 e ^{x}})

解

0

解答ステップ

x \to \infty lim (\frac{10 - 6 x ^{2}}{5 + 3 e ^{x}})

ロピタルの定理を適用する

= x \to \infty lim (\frac{- 12 x}{3 e ^{x}})

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

= \frac{- 12}{3} \cdot x \to \infty lim (\frac{x}{e ^{x}})

簡素化

= (- 4) \cdot x \to \infty lim (\frac{x}{e ^{x}})

ロピタルの定理を適用する

= (- 4) \cdot x \to \infty lim (\frac{1}{e ^{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= (- 4) \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{x} )}

x \to \infty lim (1) = 1

x \to \infty lim (e^{x}) = \infty

= (- 4) \frac{1}{\infty}

簡素化

(- 4) \frac{1}{\infty} : 0

= 0

グラフ

人気の例

limit as x approaches 0 of (arccot(x))/x

x \to 0 lim (\frac{arccot ( x )}{x})

limit as x approaches 0 of (sin(x)-arctan(x))/(x^2ln(1+x))

x \to 0 lim (\frac{sin ( x ) - arctan ( x )}{x ^{2} ln ( 1 + x )})

limit as x approaches 5 of x+5

x \to 5 lim (x + 5)

limit as x approaches 1 of (3x+2)/(1-x)

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

limit as x approaches 0 of sec(x)-tan(x)

x \to 0 lim (sec (x) - tan (x))