Find the Maclaurin polynomial p3(x) for f(x)=5x .

The Maclaurin series for a function f(x) is given by the formula:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

The Maclaurin series is just the Taylor series centered at x = 0.

Given f(x) = 5x, we can find its derivatives:

f'(x) = 5, f''(x) = 0, f'''(x) = 0.

Substituting these into the Maclaurin series formula gives:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! = 0 + 5x + 0 + 0 = 5x.

So, the Maclaurin polynomial p3(x) for f(x) = 5x is p3(x) = 5x.

The Maclaurin series for a function f(x) is given by:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

The Maclaurin series is just the Taylor series centered at zero.

Given f(x) = 5x, we can find the derivatives at zero:

f(0) = 5*0 = 0 f'(0) = 5 f''(0) = 0 f'''(0) = 0

Substituting these values into the Maclaurin series gives:

p3(x) = 0 + 5x + 0x^2/2! + 0x^3/3! = 5x

So, the Maclaurin polynomial p3(x) for f(x) = 5x is p3(x) = 5x.