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:
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?

  1. 👍
  2. 👎
  3. 👁
  1. 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.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Technology

    When using a line graph, why is it inportant to only graph 1 - 3 series of data? A line graph in Microsoft Excel will not allow you to graph more than 3 series of data. It will not show changes over time of you use more than 3

  2. Calculus

    By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B)

  3. Calculus

    Which of the following statements is true for the series the summation from n=0 to infinity of (-1)^n and 5/4^n? a) The series diverges because it is geometric with r = 5/4 and a = –1. b) The series converges to 4 because it is

  4. Math

    An arithmetic series has first term -50 and common difference 4. How many terms are in the series so that the sum of the series first exceeds 100?

  1. Chemistry (Need) 7:00

    What characterizes the electron configurations of transition metals such as silver and iron? Thanks Alot in Advance.. Fe is in the 3d transition series and Ag is in the 4d series. Thus, the distinguishing electron for the 3d

  2. Calculus - Taylor #2

    Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) =

  3. Calculus - Alternating Series Test

    Determine whether the infinite series, sigma(((-1)^(n+1))/n)^2 converges or diverges. My professor gave these in a problem set after he taught the alternating series test. Simplying the series we get, sigma(((-1)^(n+1))/n)^2

  4. calculus

    Use multiplication of power series to find the first three non-zero terms of the Maclaurin series of e^x ln(1 − x).

  1. Math

    A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.

  2. Circuits2

    A series circuit containing a 295 microfarad capacitor and a coil whose resistance and inductance are 3 ohms and 4.42 mH, respectively are supplied by the following series connected generators: 35 V at 60 Hz, 10 V at 180 Hz and 8

  3. Algebra

    Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is

  4. math

    The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

You can view more similar questions or ask a new question.