What is taylor 1e^x ?

The answer to taylor 1e^x is 1+x+1/2 x^2+1/6 x^3+1/24 x^4+\ldots

Popular >

taylor 1e^x

taylor

1 e^{x}

1 + x + \frac{1}{2} x^{2} + \frac{1}{6} x^{3} + \frac{1}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( 1 \cdot e ^{x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 1 \cdot e ^{x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 1 \cdot e ^{x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{1}{4 !} x^{4} + \dots

Refine

= 1 + x + \frac{1}{2} x^{2} + \frac{1}{6} x^{3} + \frac{1}{24} x^{4} + \dots

y d x + (y cos (\frac{x}{y}) - x) d y = 0

x \to 4 lim (3 x + 2)

\frac{d ^{4}}{d x ^{4}} (15 e^{x^{2}})

\int_{- 2}^{2} (x + 9) 4 - x^{2} d x

x \to 0 lim (\frac{8 ^{x} - 1 4 ^{x}}{x})

What is taylor 1e^x ?
The answer to taylor 1e^x is 1+x+1/2 x^2+1/6 x^3+1/24 x^4+\ldots