What is taylor x^x,1 ?

The answer to taylor x^x,1 is 1+(x-1)+(x-1)^2+1/2 (x-1)^3+1/3 (x-1)^4+\ldots

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taylor x^x,1

taylor

x^{x}, 1

1 + (x - 1) + (x - 1)^{2} + \frac{1}{2} (x - 1)^{3} + \frac{1}{3} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} (x - 1) + \frac{2}{2 !} (x - 1)^{2} + \frac{3}{3 !} (x - 1)^{3} + \frac{8}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + (x - 1) + (x - 1)^{2} + \frac{1}{2} (x - 1)^{3} + \frac{1}{3} (x - 1)^{4} + \dots

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

\int \frac{1}{( x ^{2} - 100 ) ^{2}} d x

\int \frac{3 ^{- x}}{x} d x

y (x + 1) + y^{^{'}} = 0, y (- 2) = 1

\frac{\partial}{\partial y} (2 x^{3} y)

What is taylor x^x,1 ?
The answer to taylor x^x,1 is 1+(x-1)+(x-1)^2+1/2 (x-1)^3+1/3 (x-1)^4+\ldots