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人気のある微分積分 >

limit as x approaches 0 of (12^x-13^x)/x

解

x \to 0 lim (\frac{1 2 ^{x} - 1 3 ^{x}}{x})

解

ln (12) - ln (13)

+1

十進法表記

- 0.08004 \dots

解答ステップ

x \to 0 lim (\frac{1 2 ^{x} - 1 3 ^{x}}{x})

ロピタルの定理を適用する

= x \to 0 lim (\frac{1 2 ^{x} ln ( 12 ) - 1 3 ^{x} ln ( 13 )}{1})

値を挿入する

x = 0

= \frac{1 2 ^{0} ln ( 12 ) - 1 3 ^{0} ln ( 13 )}{1}

簡素化

\frac{1 2 ^{0} ln ( 12 ) - 1 3 ^{0} ln ( 13 )}{1} : ln (12) - ln (13)

= ln (12) - ln (13)

グラフ

人気の例

limit as x approaches 0 of (sin(10x))/(sin(8x))

x \to 0 lim (\frac{sin ( 10 x )}{sin ( 8 x )})

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