2100 1- 8 Sheets 2018.pdf
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E
TUTURIAL SHEETS MATH 2100 1-8
AUTHOR MONDE LIKE MAKETO UNZA 8/6/2018
𝑒𝑥 = 1 +
𝑥 𝑥2 𝑥3 + + +⋯ , 1! 2! 3!
∫∞ 𝑒 −𝑥 −∞
2
∞
𝑑𝑥 = [∫ 𝑒
−𝑥 2
−∞ 2𝜋
∞
𝑑𝑥 ∫ 𝑒
1/2 −𝑦 2
𝑑𝑦]
−∞ ∞
1/2 2
∫ 𝑒 −𝑟 𝑟 𝑑𝑟 𝑑𝜃 ]
= [∫ 0
0 1/2
∞
= [𝜋 ∫ 𝑒 0
= √𝜋
−∞ < 𝑥 < ∞
−𝑢
𝑑𝑢]
TUTURIAL SHEETS MATH 2100 1-8
AUTHOR MONDE LIKE MAKETO UNZA 8/6/2018
𝑒𝑥 = 1 +
𝑥 𝑥2 𝑥3 + + +⋯ , 1! 2! 3!
∫∞ 𝑒 −𝑥 −∞
2
∞
𝑑𝑥 = [∫ 𝑒
−𝑥 2
−∞ 2𝜋
∞
𝑑𝑥 ∫ 𝑒
1/2 −𝑦 2
𝑑𝑦]
−∞ ∞
1/2 2
∫ 𝑒 −𝑟 𝑟 𝑑𝑟 𝑑𝜃 ]
= [∫ 0
0 1/2
∞
= [𝜋 ∫ 𝑒 0
= √𝜋
−∞ < 𝑥 < ∞
−𝑢
𝑑𝑢]
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