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Second-order taylor polynomial

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Reference no: EM131259099

a) Give the second-order Taylor polynomial P2(x)for the function f(x)=x^2*ln(x), about a=1.

b) Use Taylor's Theorem to give the Remainder Term R2(x)=f(x)-P2(x), as a function of x and some zbetween 1 and x.

c) Use the fact that 1<z<x,and the fact that 0<ln(z)<1 for all 1<z<2, to find an upper bound on R2(x)when 1<x<2. Enter this bound as a function involving x (but not z).

d) Use the upper bound to enter a value p for which |R2(x)|<0.001 for all 1< x < p.

Reference no: EM131259099

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