taylor u^2

Solution

taylor

u^{2}

u^{2}

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d u} ( u ^{2} ) ( 0 )}{1 !} u + \frac{\frac{d ^{2}}{d u ^{2}} ( u ^{2} ) ( 0 )}{2 !} u^{2} + \frac{\frac{d ^{3}}{d u ^{3}} ( u ^{2} ) ( 0 )}{3 !} u^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} u + \frac{2}{2 !} u^{2} + \frac{0}{3 !} u^{3} + \frac{0}{4 !} u^{4} + \frac{0}{5 !} u^{5} + \frac{0}{6 !} u^{6} + \frac{0}{7 !} u^{7} + \frac{0}{8 !} u^{8} + \frac{0}{9 !} u^{9} + \frac{0}{10 !} u^{10}

Refine

= u^{2}

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