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# Taylor polynomial

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2a. Find the second order Taylor polynomial for f(x) = x^(1/3) about x = x0, x0 > 0.

2b. Show that the function G(x) is differentiable at x0 and find G'(x0).

3a. Find an expression for the lower sum L(f,D) and upper sum U(f,D).

3b. Determine the lower integral and upper integral.

Please refer to the attached images for details on these questions.

##### Solution Summary

Taylor polynomial is assessed for the low and upper sums.

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Please see the attachment for solutions.

Solution:

(a) We will express first the given function in a more convenient way:
(1)
One applies now the formula of the binomial expansion, which is a power series about :
(2)
which is valid for
(3)
Substituting (z) by and () by 1/3, we will get:

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