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For the function 1/(1-x) the Taylor polynomial of degree 3 about x=0 is:

p(x) = 1 + x + x^2 + x^3

a. Find an upper bound on l R(x) l if x = 0.5

b. Write down the first three non-zero terms of the Taylor series for

g(x) = 1/(4-x^2)

Is there an easier way to do b other than finding the 2nd, 3rd, etc derivatives, because I'm getting completely confused with this?

2. Let f(x) = x^5 - 20x + 5

The real solutions are +/-sqrt2

Find the maximum and minimum value of f(x) for 0 is less than or equal to x, which is less than or equal to 2.

I just can't remember how to do this.

Thank you

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# Homework Help: Differential calculus questions

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