taylor x^2

Solution

taylor

x^{2}

x^{2}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x^{2}

y^{^{'}} - \frac{9}{x} y = \frac{( y ^{4} )}{x ^{16}}, y (1) = 1

(1 + e^{x}) y \frac{d y}{d x} = e^{x}

\int \frac{1}{256 + x ^{2}} d x

e^{x c o s (2 x)}

\frac{d r}{d θ} = \frac{r ^{2} + 9 r θ ^{2}}{3 θ ^{3}}