Is it possible to find a Maclaurinexpansion for (a) f(x) = sqrt x or (b) f(x) =s

Question

Is it possible to find a Maclaurinexpansion for (a) f(x) = sqrt x or (b) f(x) =sqrt 1+ x ? Explain.

(a) Choose the correct answer below.

(A) Yes. Every term of the Maclaurin expansion for f(x) = sqrt x

(B) No. While f(x) = sqrt x is defined at x =0, none of the derivatives of f(x) =sqrt x are defined at x = 0. Therefore Maclaurin expansion is undefined for this function.

(C) NO. Neither the function nor it's derivatives are defined at x=0. Therefore, the Maclaurin expansion is undefined for this function.

(D) No. Even thought he derivatives of f(x) = sqrt x are defined at x =0, f(x)=sqrt x is not defined at x=0. Therefore, the Maclaurin expansion is undefined for this function.

(b) Choose the correct answer below.

(A) Yes, Every term of the Maclaurin expansionis defined for f(x) = sqrt 1 + x

(B) No. Neither the function nor its derivatives are defined at x =0. Therefore, the Maclaurin expansion is undefined for f(x) = sqrt 1+x

(C) No. Even though the derivatives of f(x)=sqrt 1+x are defined T x = 0, f(x)=sqrt 1+x is not defined at x=0. Therefore the Maclaurin expansion is not defined for this function

(D) No. While f(x)= sqrt 1+x =0, none of the derivatives of f(x)=sqrt 1+ are defined at x=0. Therefore, Maclaurin expansion is undefined for this function.

Explanation / Answer

a)

(B) No. While f(x) = sqrt x is defined at x =0, none of the derivatives of f(x) =sqrt x are defined at x = 0. Therefore Maclaurin expansion is undefined for this function.

b) (A)Yes, Every term of the Maclaurin expansionis defined for f(x) = sqrt 1 + x

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