taylor 3x

Solution

taylor

3 x

3 x

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{3}{1 !} x + \frac{0}{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

= 3 x

\frac{\partial}{\partial x} (x^{2} + 4 y^{2})

\int sin (x) cos (x) x d x

x \to 1 + lim (\frac{5 x + 6}{x - 1})

x = - 5, x = 1, y = 7 x, y = x^{2} - 8

t^{3} + 1 t, at t = 1