Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function. 5e^(-x)^2 cos(4x)

The first three nonzero terms in the Maclaurin series is

Step-by-step explanation:

GIven that:

The Maclaurin series of cos x can be expressed as :

From equation(1), substituting x with (4x), Then:

The first three terms of cos (4x) is:

Multiplying equation (2) with (3); we have :

Finally , multiplying 5 with ; we have:

The first three nonzero terms in the Maclaurin series is

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)