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Hi f (x) = sqrt(9-2x) g(x) =...

Hi

f (x) = sqrt(9-2x)

g(x) = sqrt(1-2x)

a) by writing sqrt(9-2x) = 3 sqrt(1-2/9x),

and using substitution in one of the standard Taylor series given in the module, find the Taylor series about 0 for f. Give explicitly all terms up to the term in x^3. Determine a range of validity for this Taylor series.

b) Use the answer from part (a), and the fact that 1-2x = 9-2(x+4), to find the Taylor series about -4 for g. Give explicitly the same number of terms as in part (a). Determine a range of validity for this Taylor series.

c) Check the first four terms in the Taylor series that you found in part (b) by finding the 1st, 2nd and 3rd derivatives of g, and using these to find the cubic Taylor polynomial about -4 for g.

Cheers

A

f (x) = sqrt(9-2x)

g(x) = sqrt(1-2x)

a) by writing sqrt(9-2x) = 3 sqrt(1-2/9x),

and using substitution in one of the standard Taylor series given in the module, find the Taylor series about 0 for f. Give explicitly all terms up to the term in x^3. Determine a range of validity for this Taylor series.

b) Use the answer from part (a), and the fact that 1-2x = 9-2(x+4), to find the Taylor series about -4 for g. Give explicitly the same number of terms as in part (a). Determine a range of validity for this Taylor series.

c) Check the first four terms in the Taylor series that you found in part (b) by finding the 1st, 2nd and 3rd derivatives of g, and using these to find the cubic Taylor polynomial about -4 for g.

Cheers

A

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