Answer:
Alright. The first few non-zero terms of the Maclaurin series for f(x) = ln(1 + 7x) are:
f(x) = 7x - 24.5x^2 + 85.75x^3 - 300.125x^4 + ...
So the first four non-zero terms would be:
f(x) = 7x - 24.5x^2 + 85.75x^3 - 300.125x^4
Explanation:
Sure, I can help you with that.
The Maclaurin series for ln(1+x) is:
ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...
Therefore, we just need to replace x with 7x and write the first four nonzero terms:
ln(1+7x) = 7x - (49x^2)/2 + (343x^3)/3 - (2401x^4)/4 + ...
So the first four nonzero terms of the Maclaurin series for ln(1+7x) are:
7x - (49x^2)/2 + (343x^3)/3 - (2401x^4)/4