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

The answer to taylor 4+x^2+4x^4,-3 is 337-438(x+3)+217(x+3)^2-48(x+3)^3+4(x+3)^4

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

taylor

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

337 - 438 (x + 3) + 217 (x + 3)^{2} - 48 (x + 3)^{3} + 4 (x + 3)^{4}

Solution steps

Apply the Taylor Formula

= 337 + \frac{\frac{d}{d x} ( 4 + x ^{2} + 4 x ^{4} ) ( - 3 )}{1 !} (x + 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 + x ^{2} + 4 x ^{4} ) ( - 3 )}{2 !} (x + 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 + x ^{2} + 4 x ^{4} ) ( - 3 )}{3 !} (x + 3)^{3} + \dots

Evaluate Derivatives

= 337 + \frac{- 438}{1 !} (x + 3) + \frac{434}{2 !} (x + 3)^{2} + \frac{- 288}{3 !} (x + 3)^{3} + \frac{96}{4 !} (x + 3)^{4}

Refine

= 337 - 438 (x + 3) + 217 (x + 3)^{2} - 48 (x + 3)^{3} + 4 (x + 3)^{4}

What is taylor 4+x^2+4x^4,-3 ?
The answer to taylor 4+x^2+4x^4,-3 is 337-438(x+3)+217(x+3)^2-48(x+3)^3+4(x+3)^4