Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 25, Problem 9P
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Students have asked these similar questions
Using FDF, BDF, and CDF, find the first derivative;
1. The distance x of a runner from a fixed point is measured (in meters) at an
interval of half a second. The data obtained is:
t
0
x
0
0.5
3.65
1.0
1.5
2.0
6.80
9.90
12.15
Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s
2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input
of 2 assuming a step size of 1. Calculate using Analytical Solution and
Absolute Relative Error:
=
True Value - Approximate Value|
x100
True Value
3. Given the data below where f(x)
sin (3x), estimate f(1.5) using Langrage
Interpolation.
x
1
1.3
1.6
1.9
2.2
f(x)
0.14
-0.69
-0.99
-0.55
0.31
4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given
by:
30
x =
Loo (2000ln
140000
140000
-
2100
9.8t) dt
Using the Trapezoidal Rule, n=2, find the distance covered.
5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the
results for n=4 and n=8
1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat
over one period may be approximated by the function,
f(x)
=
0.005x4
2
0.005x³-0.364x² + 1.27x
on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from
that used in any other posts on this topic, to generate a periodic function that can be used to model its heartbeat, and graph your
result. Be sure to include your chosen value of n in your Subject Heading.
7. The demand for a product, in dollars, is
p = D(x) = 1000 -0.5 -0.0002x²
1
Find the consumer surplus when the sales level is 200.
[Hints: Let pm be the market price when xm units of product are sold. Then the consumer
surplus can be calculated by foam (D(x) — pm) dx]
Chapter 25 Solutions
Numerical Methods for Engineers
Ch. 25 - Solve the following initial value problem over the...Ch. 25 - Solve the following problem over the interval from...Ch. 25 - Use the (a) Euler and (b) Heun (without iteration)...Ch. 25 - Solve the following problem with the fourth-order...Ch. 25 - Solve from t=0to3withh=0.1 using (a) Heun (without...Ch. 25 - 25.6 Solve the following problem numerically from...Ch. 25 - Use (a) Eulers and (b) the fourth-order RK method...Ch. 25 - 25.8 Compute the first step of Example 25.14...Ch. 25 -
25.9 If, determine whether step size adjustment...Ch. 25 - Use the RK-Fehlberg approach to perform the same...
Ch. 25 -
25.11 Write a computer program based on Fig....Ch. 25 - Test the program you developed in Prob. 25.11 by...Ch. 25 -
25.13 Develop a user-friendly program for the...Ch. 25 - Develop a user-friendly computer program for the...Ch. 25 - Develop a user-friendly computer program for...Ch. 25 - 25.16 The motion of a damped spring-mass system...Ch. 25 - If water is drained from a vertical cylindrical...Ch. 25 - The following is an initial value, second-order...Ch. 25 - Assuming that drag is proportional to the square...Ch. 25 - A spherical tank has a circular orifice in its...Ch. 25 - The logistic model is used to simulate population...Ch. 25 - 25.22 Suppose that a projectile is launched...Ch. 25 - The following function exhibits both flat and...Ch. 25 - 25.24 Given the initial conditions,, solve the...Ch. 25 - Use the following differential equations to...Ch. 25 - 25.26 Three linked bungee jumpers are depicted in...
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- 8. Given the rate of net investment I(t) = 9t¹/2, find the level of capital formation in (i) 16 years and (ii) between the 4th and the 8th years.arrow_forward9. If the marginal revenue function of a firm in the production of output is MR = 40 - 10q² where q is the level of output, and total revenue is 120 at 3 units of output, find the total revenue function. [Hints: TR = √ MRdq]arrow_forward6. Solve the following first-order linear differential equations; if an initial condition is given, definitize the arbitrary constant: (a) 2 + 12y + 2et = 0, y(0) = /; (b) dy+y=tarrow_forward
- 4. Let A = {a, b, c, d, e, f}, B = {e, f, g, h} and C = {a, e, h,i}. Let U = {a, b, c, d, e, f, g, h, i, j, k}. • Draw a Venn Diagram to describe the relationships between these sets Find (AB) NC • Find (AC) UB Find AUBUC • Find (BC) N (A - C)arrow_forward7. A consumer lives on an island where she produces two goods x and y according to the production possibility frontier x² + y² < 200 and she consumes all the goods. Her utility function is U(x, y) = x y³. She faces an environmental constraint on her total output of both goods. The environmental constraint is given by x + y ≤20. • (a) Write down the consumer's optimization problem. (b) Write out the Kuhn-Tucker first order conditions. (c) Find the consumer's optimal consumption bundle (x*, y*).arrow_forward3. Answer the following questions: (a) Given the marginal propensity to import M'(Y) = 0.1 and the information that M = 20 when Y = 0, find the import function M(Y). (b) Given a continuous income stream at the constant rate of $1,000 per year, what will be the present value II if the income stream terminates after exactly 3 years and the discount rate is 0.04? (c) What is the present value of a perpetual cash flow of $2,460 per year, discounted at r = 8%?arrow_forward
- 5. Let A and B be arbitrary sets. Prove AnB = AUB.arrow_forward2. Answer the following questions: (a) Given the marginal-revenue function R'(Q) = 28Q - €0.3Q, find the total-revenue function R(Q). What initial condition can you introduce to definitize the constant of integration? = (b) Given the marginal propensity to consume C'(Y) 0.80.1Y-1/2 and the information that C = Y when Y = 100, find the consumption function C(Y).arrow_forward7. Let X, A, and B be arbitrary sets such that ACX and BC X. Prove AUB CX.arrow_forward
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