簡約 1/(sqrt(2pi))e^{-1/2*0.1^2}

解

簡約

\frac{1}{2 π} e^{- \frac{1}{2} \cdot 0. 1^{2}}

0.39695 \dots

解答ステップ

\frac{1}{2 π} e^{- \frac{1}{2} \cdot 0. 1^{2}}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{2 π} \cdot \frac{1}{e ^{0. 1^{2} \cdot \frac{1}{2}}}

\frac{1}{2 π} = \frac{1}{2 π}

= \frac{1}{2 π} \cdot \frac{1}{e ^{0. 1^{2} \cdot \frac{1}{2}}}

\frac{1}{e ^{\frac{1}{2} \cdot 0. 1^{2}}} = \frac{1}{e ^{0.005}}

= \frac{1}{e ^{0.005}} \cdot \frac{1}{2 π}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 π e ^{0.005}}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 e ^{0.005} π}

元を10進法形式に変換する

2 = 1.41421 \dots

= \frac{1}{1.41421 \dots e ^{0.005} π}

元を10進法形式に変換する

π = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{0.005}}

e^{0.005} = 1.00501 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots \cdot 1.00501 \dots}

数を乗じる:

1.41421 \dots \cdot 1.77245 \dots \cdot 1.00501 \dots = 2.51919 \dots

= \frac{1}{2.51919 \dots}

数を割る:

\frac{1}{2.51919 \dots} = 0.39695 \dots

= 0.39695 \dots