# GATE2007-IT-22

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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

retagged

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

edited
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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