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人気のある微分積分 >

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

解

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

解

9 π

+1

十進法表記

28.27433 \dots

解答ステップ

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

ロピタルの定理を適用する

= x \to 3 lim (\frac{2 ( x - 3 ) + cos ( π x ) π}{- \frac{1}{x ^{2}}})

値を挿入する

x = 3

= \frac{2 ( 3 - 3 ) + cos ( π 3 ) π}{- \frac{1}{3 ^{2}}}

簡素化

\frac{2 ( 3 - 3 ) + cos ( π 3 ) π}{- \frac{1}{3 ^{2}}} : 9 π

= 9 π

グラフ

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