(1 point) Suppose that f(x) and g(x) are given by the power series f(x)=6+7x+3x2+5x3+⋯ and g(x)=7+8x+3x2+4x3+⋯. By multiplying power series, find the first few terms of the series for the product h(x)=f(x)⋅g(x)=c0+c1x+c2x2+c3x3+⋯.

The value of , ,  ,   and so on and this can be determined by using the arithmetic operations.

Given :

f(x) and g(x) are given by the power series f(x)=6+7x+3x2+5x3+⋯ and g(x)=7+8x+3x2+4x3+⋯.

Given that f(x) = 6+7x+3+5+⋯ and g(x) = 7+8x+3+4+⋯. So, the following calculation can be used in order to multiply the power series.

   --- (1)

Now, the generalized power series is given by the equation:

   ---- (2)

Now comparing equation (1) and equation (2).

and so on.

For more information, refer to the link given below:

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f(x).g(x)   =  c0+c1x+c2x2+c3x3+⋯.

c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...…...

Step-by-step explanation:

Suppose that f(x) and g(x) are given by the power series

f(x)=6+7x+3x2+5x3+⋯ and

g(x)=7+8x+3x2+4x3+⋯

By multiplying power series ,

f(x).g(x) = (6+7x+3x2+5x3+⋯).(7+8x+3x2+4x3+⋯)

           = 6(7+8x+3x2+4x3+⋯)+7x(7+8x+3x2+4x3+⋯)+3x2(7+8x+3x2+4x3+⋯) + 5x3(7+8x+3x2+4x3+⋯)+......

f(x).g(x)   =  c0+c1x+c2x2+c3x3+⋯.is the form

c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...……

$9.41

step-by-step explanation: