Taylor Polynomial

sony

Hi

I have found the following TP (n=4) for g(x) = (1+5x)^1/5
P4(x) = 1+x-2x^2+6x^3-21x^4

Then they ask me to show that 0<E4(x)<80x^5 when x>0.

I don't know how to start, or exactly what Im supposed to show...?

I have found E4(x) to be( 399/[5(1+5X)^24/5] ) *x^5...

And 0<X<x ...?

HallsofIvy

To show that the error is LESS than something, you want to think about the X that gives the LARGEST possible error. Since X is in the denominator, the largest value of the fraction will be when X= 0. If you take X= 0 what is that value in the parentheses? (Gosh, 399 is awful close to 400!)

sony

Oh now I see how I get 0<E4(x)<80x^5

Thanks!