search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
0 votes
694 views

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
retagged by
694 views

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


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.
Answer:

Related questions

1 vote
1 answer
1
516 views
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)
asked Nov 3, 2014 in Numerical Methods Ishrat Jahan 516 views
4 votes
1 answer
2
683 views
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 following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the sequence $x_n$ converges for all ... $a < x_0 < b$? $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
asked Oct 31, 2014 in Numerical Methods Ishrat Jahan 683 views
0 votes
1 answer
3
678 views
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 width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
asked Sep 29, 2014 in Numerical Methods Kathleen 678 views
5 votes
1 answer
4
1.7k views
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/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or equal ... using the Simpson's rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
asked Sep 28, 2014 in Numerical Methods jothee 1.7k views
...