Please post the whole question.
I have a result for part a) which is
1+(3/2*x)+((27/16)*x^2)+((27/16)*x^3)+......
using this and the fact that 1-3x=4-3(x+1) i need to find a taylor series for
g(x) =[16/(1-3x)^2]
I know its by substitution but I just don't know where to start.
I did post part a of this question but I was confident in what I was doing - this I haven't got clue as once I have resolved this I need to check first four terms in the Taylor series by finding first, second and third derivatives.
If your answer a is correct (is that sure? Or? ...) than you can do (like you said) a substitution, if you say: x+1=t
Then you get: 16/(4-3t)^2, this is exactly the same as f(x).
EDIT:
I checked, question a seems right, I guess you've used the binomial serie?
This is what I think, for your first exercice you have calculated the Taylor serie about 0 for f (so practically an maclaurin serie).
(this is just an approximation)
Now you have to use this answer and the fact that .
If you say: then you get this for the function .
Do you notice any relation with ? ...