Register

GATE IT 2007 | Question: 22

• retagged by
2,350 views
0 0 votes

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

1 Answer

3 3 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

• edited by
Voting & Accepting an answer helps improve the community
Answer:
← Previous · GATE IT 2007 | Quest...Next → · GATE IT 2007 | Quest...
← Previous in category · Is the value obtaine...Next in category → · GATE IT 2007 | Quest...
Position:
Show:

Related questions

0 0 votes
1 1 answer
2.7k
2.7k views
Kathleen asked Sep 29, 2014
2,695 views
GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f&rsquo;&rsquo;(x), x \in [a, b]$ where $h$ is the widt...
1 1 vote
1 1 answer
2.6k
2.6k views
Ishrat Jahan asked Nov 3, 2014
2,592 views
GATE IT 2005 | Question: 2
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtainedis always (1/3)is always < (1/3)is always = (1/3)may be ...
6 6 votes
1 1 answer
2.7k
2.7k views
Ishrat Jahan asked Oct 30, 2014
2,688 views
GATE IT 2007 | Question: 77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c 0$.For which of the f...
5 5 votes
1 1 answer
4.9k
4.9k views
go_editor asked Sep 28, 2014
4,852 views
GATE CSE 2014 | Set 3 | Question: 46
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/ar...