taylor 5x

Solution

taylor

5 x

5 x

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 5 x ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 x ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 x ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{5}{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

= 5 x

x y^{^{'}} - 4 y = x^{6} e^{x}

x \to \infty lim (\frac{x ^{99}}{e ^{x}})

\int_{1}^{a} (\frac{1}{4 x}) d x

e^{s i n (x)} cos (x)

x \to - 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})