calculus

posted by .

use the power series to estimate the series:
from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error.

I found the 'terms' in the series to be:
x-(1/2)x^2+(1/3)x^3-(1/4)x^4......
with a radius of convergence of 1

I found when I plugged in 0, I got 0
how do I find the error less than .0001?

• calculus -

You need to insert te upper limit in the series, the lower limit and then subtract. However, in this that doesn't work as the series doesn't converge at the upper limit.

What you need to do is to write down the series that converges for x larger than one and the series that converges for x smaller than one, integrate both and then add up the integral of the former from x = 1 to x = 4 and the integral of the latter from x = 0 to x = 1.

Similar Questions

1. Chemistry

How do you find Absolute error and how do you find relative error?
2. calculus - power series ASAP please :)

using power series, integrate & evaluate to 4 dec. places integral from 0 to 1: sin x^2 dx i'm REALLY stuck on this. and i need help asap.. what is the inverse of "sin x^2" so that i could have it in a fraction that will fit the power …
3. Calculus

Estimate delta(x) using the Linear Approximation and use a calculator to compute both the error and the percentage error. f(x)=cosx a=(pi/4) delta(x)=.06 delta(x)= ______ i got this part and it's -.04242 The error in Linear Approximation …
4. calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... …
5. Economics

Economyst, please help Rubax__ a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales: Qt= a + bt + c1D1 + c2D2 + c3D3 Where Qt= sales of athletic shoes in the tth quarter t= 1, 2,…., 28[2001(I), …

Economyst, please help Rubax__ a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales: Qt= a + bt + c1D1 + c2D2 + c3D3 Where Qt= sales of athletic shoes in the tth quarter t= 1, 2,…., 28[2001(I), …
7. Calculus

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area?
8. Calc II

Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, …
9. Integral Calculus

We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer …
10. calculus

Approximate the value of the series to within an error of at most 10^−5. The infinite series from n=1 to infinity (−1)^(n+1)/(n^6) according to the equation (2): |S_n - S| is less than or equal to a_(n+1) what is the smallest value …

More Similar Questions