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人気のある微分積分 >

limit as h approaches 0 of ((8(1/2+h)^8-8(1/2)^8))/h

解

h \to 0 lim \frac{( 8 ( \frac{1}{2} + h ) ^{8} - 8 ( \frac{1}{2} ) ^{8} )}{h}

解

\frac{1}{2}

+1

十進法表記

0.5

解答ステップ

h \to 0 lim (\frac{8 ( \frac{1}{2} + h ) ^{8} - 8 ( \frac{1}{2} ) ^{8}}{h})

簡素化

\frac{8 ( \frac{1}{2} + h ) ^{8} - 8 ( \frac{1}{2} ) ^{8}}{h} : \frac{256 ( \frac{1}{2} + h ) ^{8} - 1}{32 h}

= h \to 0 lim (\frac{256 ( \frac{1}{2} + h ) ^{8} - 1}{32 h})

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

= \frac{1}{32} \cdot h \to 0 lim (\frac{256 ( \frac{1}{2} + h ) ^{8} - 1}{h})

256 (\frac{1}{2} + h)^{8}

を

256 (\frac{1}{2} + h)^{8} - 1 : 256 (\frac{1}{2} + h)^{8} (1 - \frac{1}{256 ( \frac{1}{2} + h ) ^{8}})

からくくり出す

= \frac{1}{32} \cdot h \to 0 lim \frac{256 ( \frac{1}{2} + h ) ^{8} ( 1 - \frac{1}{256 ( \frac{1}{2} + h ) ^{8}} )}{h}

簡素化

\frac{256 ( \frac{1}{2} + h ) ^{8} ( 1 - \frac{1}{256 ( \frac{1}{2} + h ) ^{8}} )}{h} : 2 (4 h^{2} + 4 h + 22 h + 2 + 2) (4 h^{2} + 4 h - 22 h + 2 - 2) (4 h^{2} + 4 h + 2) (2 h + 2)

= \frac{1}{32} \cdot h \to 0 lim (2 (4 h^{2} + 4 h + 22 h + 2 + 2) (4 h^{2} + 4 h - 22 h + 2 - 2) (4 h^{2} + 4 h + 2) (2 h + 2))

値を挿入する

h = 0

= \frac{1}{32} \cdot 2 (4 \cdot 0^{2} + 4 \cdot 0 + 22 \cdot 0 + 2 + 2) (4 \cdot 0^{2} + 4 \cdot 0 - 22 \cdot 0 + 2 - 2) (4 \cdot 0^{2} + 4 \cdot 0 + 2) (2 \cdot 0 + 2)

簡素化

\frac{1}{32} \cdot 2 (4 \cdot 0^{2} + 4 \cdot 0 + 22 \cdot 0 + 2 + 2) (4 \cdot 0^{2} + 4 \cdot 0 - 22 \cdot 0 + 2 - 2) (4 \cdot 0^{2} + 4 \cdot 0 + 2) (2 \cdot 0 + 2) : \frac{1}{2}

= \frac{1}{2}

グラフ

人気の例

limit as a approaches-2 of (a^3+8)/(a+2)

a \to - 2 lim (\frac{a ^{3} + 8}{a + 2})

limit as x approaches 0+of 3x+2

x \to 0 + lim (3 x + 2)

limit as x approaches 3 of (x-3)csc(pix)

x \to 3 lim ((x - 3) csc (π x))

limit as x approaches-1/2 of x

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

limit as x approaches-infinity of x-x^2

x \to - \infty lim (x - x^{2})