Taylor Polynomials

Determine the third Taylor Polynomial of f(x) at x=0 for the function

f(x)=(x+1)^-1/2

My answer is:

p(x)=1+1/2x+3/8x^2+5/16x^3

Is this correct, and is it called the third Taylor polynomial because it ends in x^3? Also, is the p(x) correct or should it be written another way?

Quote:

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Originally Posted by Foxtenn5

Determine the third Taylor Polynomial of f(x) at x=0 for the function

f(x)=(x+1)^-1/2

My answer is:

p(x)=1+1/2x+3/8x^2+5/16x^3

Is this correct, and is it called the third Taylor polynomial because it ends in x^3? Also, is the p(x) correct or should it be written another way?

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You're not quite right. Your coefficients are correct except that two of them should be negative. But as for the degree of the polynomial, it is correct.

Quote:

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Originally Posted by icemanfan

You're not quite right. Your coefficients are correct except that two of them should be negative. But as for the degree of the polynomial, it is correct.

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Oh, so should it be

p(x)=1-1/2x+3/8x^2-5/16x^3

Quote:

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Originally Posted by Foxtenn5

Oh, so should it be

p(x)=1-1/2x+3/8x^2-5/16x^3

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Yes, that is correct.

(Rofl) Thanks!!