What is taylor x^4-3x^2+1,1 ?

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

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taylor x^4-3x^2+1,1

taylor

x^{4} - 3 x^{2} + 1, 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

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