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Transcript
# USE of Expansion RAR 1. (1+x)ⁿ = 1+nX + n(n-1)x²/2! + n(n-1)(n-2)x³/3! +... ∞, x∈R 2. eˣ = 1 + x/1! + x²/2! +x³/3! +... ∞, x∈R 3. aˣ = 1 + x(lna)/1! + (x(lna))²/2! +... ∞ 4. ln(1+x) = x - x²/2 + x³/3 - x⁴/4 +... ∞, -1≤x≤1 e^(ix) = cosx + isinx Euler's x -> i∞ e^(ix) = 1 + ix - x²/2! - ix³/3!...
# USE of Expansion RAR 1. (1+x)ⁿ = 1+nX + n(n-1)x²/2! + n(n-1)(n-2)x³/3! +... ∞, x∈R 2. eˣ = 1 + x/1! + x²/2! +x³/3! +... ∞, x∈R 3. aˣ = 1 + x(lna)/1! + (x(lna))²/2! +... ∞ 4. ln(1+x) = x - x²/2 + x³/3 - x⁴/4 +... ∞, -1≤x≤1 e^(ix) = cosx + isinx Euler's x -> i∞ e^(ix) = 1 + ix - x²/2! - ix³/3! +... ∞, x -> ∞ cos x + isinx = (1 - x²/2! + x⁴/4! + x⁶/6! +...) + i(x - x³/3! + x⁵/5! -...)
