Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 33.4, Problem 3E
Program Plan Intro
To alter the
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An approximation to the integral of a function f(x) over an interval [a, b] can be found by first approximating f(x) by the straight line that goes through the end points (a, f(a)) and (b, f(b)), and then finding the area under the straight line, which is the area of a trapezoid. Write a function trapezint(f, a, b) that returns this approximation to the integral. Test your code by integrating cos(x) and sin(x) from 0 to π.
Algorithms Question
Three points P, Q, and R are said to be collinear if they are on a single line. To check whether the 3 points lie on the same line, we use the distance formula. If P, Q and R are three collinear points, then:
Distance from P to Q + Distance from Q to R = Distance from P to R
PQ + QR = PR
The distance between two points (x1, y1) and (x2, y2) is given by
Hence, we can easily find the distance between the points P, Q and R, with the help of this formula.
Design an algorithm (pseudocode) to check whether three points are collinear. In your solution include the input and the output.
Q10:
Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential equation.
1. The charge Q(t) on the capacitor in the electrical circuit shown satisfies the
differential equation
where
d²Q dQ 1
+R- + √ √e
dt2 dt
L = 0.5
R = 6.0
C= 0.02
and V(t) is the applied voltage.
V(t)
= V(t),
henrys is the coil's inductance
ohms is the resistor's resistance
farads is the capacitor's capacitance
ellee
(i) Is the circuit oscillatory?
(ii) If V(t) = 24 sin(10r) volts and Q(0) = 0 = Q'(0), find Q(t).
(iii) Sketch the transient solution, the steady state solution, and the full solution
Q(t).
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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