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The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$.  Consider the following values for the step size h.

  1. 10-2
  2. 10-3
  3. 10-4
  4. 10-5

For which of these values of the step size h, is the computed value guaranteed to be correct to seven decimal places. Assume that there are no round-off errors in the computation.

  1. iv only
  2. iii and iv only
  3. ii, iii and iv only
  4. i, ii, iii and iv
in Numerical Methods by Boss (16.3k points)
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1 Answer

+2 votes

error = (b-a)h2.max(f"(x) between 0 and 1) /12 

error <= 10-7

solving these equations we get

h <= 6.644*10-4

option B

by Boss (13.6k points)
edited by
+1

@Vikrant : why error <=10^-8

Why not 10^-7 ??

We need only upto 7 decimal places !!

+1
@sandeep you are right it should be 10^-7. I have edited the answer.
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