taylor v^2

Solution

taylor

v^{2}

v^{2}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= v^{2}

\frac{d}{d x} (\frac{4 e ^{4 x}}{e ^{8} ( e ^{16} - 1 )})

y = sin (x), at x = \frac{5 π}{3}

x \to 0 lim (\frac{5 ^{x} - 7 ^{x}}{x})

x \to 0 lim (\frac{x ^{2} - 3}{x})

\frac{d y}{d x} (2) - 4 x y = 8 x