taylor 1+x

Solution

taylor

1 + x

1 + x

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \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

= 1 + x

y = (4 x - 1)^{2}

\frac{d}{d x} ((3 x + 4) (- 3 + 2 x))

\int (3 x + 8)^{\frac{2}{3}} d x

\frac{d}{d x} (\frac{2}{( x - 1 ) ^{2}})

\int \frac{1 - sin ( x )}{1 + sin ( x )} d x