What is taylor arcsin(x) ?

The answer to taylor arcsin(x) is x+1/6 x^3+3/40 x^5+5/112 x^7+\ldots

taylor arcsin(x)

taylor

arcsin (x)

x + \frac{1}{6} x^{3} + \frac{3}{40} x^{5} + \frac{5}{112} x^{7} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{9}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{225}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \dots

Refine

= x + \frac{1}{6} x^{3} + \frac{3}{40} x^{5} + \frac{5}{112} x^{7} + \dots

y^{^{'}} + y = 5 cos (2 t), y (0) = 3

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

\int \frac{1}{1 - x ^{2} - 4 x} d x

0.4241 (y - 25) + 70 x = - 10845.81 \cdot \frac{d y}{d x}

\int \frac{3 x ^{3} - 2 x ^{2} + x - 5}{x ^{2}} d x

What is taylor arcsin(x) ?
The answer to taylor arcsin(x) is x+1/6 x^3+3/40 x^5+5/112 x^7+\ldots