What is taylor x^3,4 ?

The answer to taylor x^3,4 is 64+48(x-4)+12(x-4)^2+(x-4)^3

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taylor x^3,4

taylor

x^{3}, 4

64 + 48 (x - 4) + 12 (x - 4)^{2} + (x - 4)^{3}

Solution steps

Apply the Taylor Formula

= 64 + \frac{\frac{d}{d x} ( x ^{3} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{3} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{3} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

Evaluate Derivatives

= 64 + \frac{48}{1 !} (x - 4) + \frac{24}{2 !} (x - 4)^{2} + \frac{6}{3 !} (x - 4)^{3} + \frac{0}{4 !} (x - 4)^{4} + \frac{0}{5 !} (x - 4)^{5} + \frac{0}{6 !} (x - 4)^{6} + \frac{0}{7 !} (x - 4)^{7} + \frac{0}{8 !} (x - 4)^{8} + \frac{0}{9 !} (x - 4)^{9} + \frac{0}{10 !} (x - 4)^{10}

Refine

= 64 + 48 (x - 4) + 12 (x - 4)^{2} + (x - 4)^{3}

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What is taylor x^3,4 ?
The answer to taylor x^3,4 is 64+48(x-4)+12(x-4)^2+(x-4)^3