What is taylor x^4+2x,x=1 ?

The answer to taylor x^4+2x,x=1 is 3+6(x-1)+6(x-1)^2+4(x-1)^3+(x-1)^4

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taylor x^4+2x,x=1

taylor

x^{4} + 2 x, x = 1

3 + 6 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{6}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{24}{3 !} (x - 1)^{3} + \frac{24}{4 !} (x - 1)^{4}

Refine

= 3 + 6 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

y = \frac{4 x ^{2} + 8 x + 8}{x}

\frac{\partial}{\partial y} (ln (x - 4 y))

x \to 1 lim (2 x^{3} + x - 1)

f (x) =, \frac{1}{x}

f (x) = - 3 tan (x) - e^{- x}

What is taylor x^4+2x,x=1 ?
The answer to taylor x^4+2x,x=1 is 3+6(x-1)+6(x-1)^2+4(x-1)^3+(x-1)^4