taylor x

Solution

taylor

x

x

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{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

= x

\frac{d}{d x} ((x - 5) ln (\frac{x - 5}{10}))

\int \frac{1}{x 64 x ^{2} - 5} d x

\int_{- 1}^{1} (0 - y^{2} + 1) d y

12 y^{^{''}} - 12 y^{^{'}} + 30 y = 0

\int \frac{3 x ^{3}}{4 + x ^{8}} d x