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I'm trying to make the nth degree taylor polynomial for f(x)=sqrtx centered at 4 and then approximate sqrt(4.1) using the 5th degree polynomial

I know that the polynomials are found using the form:

P(x)= f(x)+f'(x)x+f''(x)x^2/2factorial.....f^n(x)x^n/nfactorial

so would P(4) just be:

f(4)+f'(4)x + f''(4)x^2/2factorial + f'''(4)x^3/3factorial...

and then would i just plug in 4.1 for x?

thanks for your help...i would also appreciate any general comments on taylor polynomials as I don't really understand them. Thanks!

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# Taylor polynomial help

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