Question

Find the first four terms of the infinite series expansion of the given function f(x)=(1 + 2x)^3/2

Answer 1

Answer: [DISCLAIMER]: All answers are rounded to the nearest hundredth of a decimal

f(1) = 5.20 ; f(2) = 14.70 ; f(3) = 27 ; f(4) = 41.57

Explanation:

f(1) = (1 + [2×1])
`^(3/2)`

f(1) = (1 + 2)
`^(3/2)`

f(1) = (3)
`^(3/2)`

f(1) ≈ 5.20

f(2) = (2 + [2×2])
`^(3/2)`

f(2) = (2 + 4)
`^(3/2)`

f(2) = (6)
`^(3/2)`

f(2) ≈ 14.70

f(3) = (3 + [2×3])
`^(3/2)`

f(3) = (3 + 6)
`^(3/2)`

f(3) = (9)
`^(3/2)`

f(3) = 27

f(4) = (4 + [2×4])
`^(3/2)`

f(4) = (4 + 8)
`^(3/2)`

f(4) = (12)
`^(3/2)`

f(4) ≈ 41.57