Question

Expand f(x, y) = sin (2x + 3y) by Taylor series expansion about center (π/2,π/3) up to 3 nonzero terms.

Answer 1

Answer:

Thus, the series equals f(a) if the coefficient c0=f(a). In addition, we would like the first derivative of the power series to equal f′(a) at x=a. Differentiating Equation 6.4 term-by-term, we see that

d

dx

(

∞

∑

n=0 cn(x−a)n)=c1+2c2(x−a)+3c3(x−a)2+⋯.

Therefore, at x=a, the derivative is

d

dx

(

∞

∑

n=0 cn(x−a)n) =c1+2c2(a−a)+3c3(a−a)2+⋯ =c1.

Therefore, the derivative of the series