What is e^{-0.8x}(1+0.8x+(0.8)/3 x^2) ?

The solution to e^{-0.8x}(1+0.8x+(0.8)/3 x^2) is (0.26666…x^2+0.8x+1)/(e^{0.8x)}

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simplify e^{-0.8x}(1+0.8x+(0.8)/3 x^2)

simplify

e^{- 0.8 x} (1 + 0.8 x + \frac{0.8}{3} x^{2})

\frac{0.26666 \dots x ^{2} + 0.8 x + 1}{e ^{0.8 x}}

Solution steps

e^{- 0.8 x} (1 + 0.8 x + \frac{0.8}{3} x^{2})

Apply exponent rule:

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

= \frac{1}{e ^{0.8 x}} (\frac{0.8}{3} x^{2} + 0.8 x + 1)

\frac{0.8}{3} x^{2} = 0.26666 \dots x^{2}

= \frac{1}{e ^{0.8 x}} (0.26666 \dots x^{2} + 0.8 x + 1)

Multiply fractions:

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

= \frac{1 \cdot ( 1 + 0.8 x + 0.26666 \dots x ^{2} )}{e ^{0.8 x}}

1 \cdot (1 + 0.8 x + 0.26666 \dots x^{2}) = 1 + 0.8 x + 0.26666 \dots x^{2}

= \frac{1 + 0.8 x + 0.26666 \dots x ^{2}}{e ^{0.8 x}}

x e^{- 0}

\frac{e ^{1}}{e ^{2}}

(6 x q^{3} r p^{6}) (4 p^{3} q^{6} x r^{2})

x^{- 5} d x

- 48456 e^{- 673}

What is e^{-0.8x}(1+0.8x+(0.8)/3 x^2) ?
The solution to e^{-0.8x}(1+0.8x+(0.8)/3 x^2) is (0.26666…x^2+0.8x+1)/(e^{0.8x)}