Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 1, Problem 37P
Repeat problem P1-36 for the data shown in Fig. P1.37.
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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 1 Solutions
Introductory Mathematics for Engineering Applications
Ch. 1 - A constant force F=2N is applied to a spring and...Ch. 1 - The spring force F and displacement x for a...Ch. 1 - The spring force F and displacement x for a...Ch. 1 - In a bolted connection shown in Fig. P1.4. the...Ch. 1 - Repeat problem P1.14 for the data given in Fig...Ch. 1 - The velocity v (t ) of a ball thrown upward...Ch. 1 - The velocity v (r ) of a ball thrown upward...Ch. 1 - A model rocket is fired in the vertical plane. The...Ch. 1 - A model rocket is fired in the vertical plane. The...Ch. 1 - The velocity of a vehicle is measured at two...
Ch. 1 - The velocity of a vehicle is measured at two...Ch. 1 - The velocity v (t ) of a vehicle during braking is...Ch. 1 - A linear trajectory is planned for a robot to pick...Ch. 1 - The acceleration of the linear trajectory of...Ch. 1 - The temperature distribution in a well-insulated...Ch. 1 - The temperature distribution in a well-insulated...Ch. 1 - The voltage-current relatonship for the cicuit...Ch. 1 - A voltage source Vs is used to apply two different...Ch. 1 - Repeat problem P1-18 for the data shown in Fig,...Ch. 1 - Repeat problem P1-18 for the data shown in Fig...Ch. 1 - A linear model of a diode is shown in Fig. P1.21....Ch. 1 - Repeat Problem P1-21 for the data given in Fig....Ch. 1 - The output voltage, v0, of the Op-Amp circuit...Ch. 1 - The output voltage, v0, of the Op-Amp circuit...Ch. 1 - A DC motor is driving an inertial load JL shown in...Ch. 1 - Repeat problem P1-25 for the data shown in Fig....Ch. 1 - In the active region, the output voltage v0 of the...Ch. 1 - Repeat problem P1-27 for the data given in Fig,...Ch. 1 - An actuator used in a prosthetic arm can produce...Ch. 1 - The following two measurements of maximum heart...Ch. 1 - The electrical activity of muscles can he...Ch. 1 - A civil engineer needs to establish the elevation...Ch. 1 - A thermocouple is a temperature measurement...Ch. 1 - The voltage across a thermocouple is calibrated...Ch. 1 - An iron-constantan thermocouple is calibrated by...Ch. 1 - Prob. 36PCh. 1 - Repeat problem P1-36 for the data shown in Fig....Ch. 1 - To determine the concentration of a purified...Ch. 1 - Repeat problem P1-38 lithe absorption-...Ch. 1 - A chemistry student is performing in experiment to...Ch. 1 - To obtain the linear relationship between the...Ch. 1 - A thermostat control with dial marking from 0 to...Ch. 1 - In a pressure-fed journal bearing, forced cooling...
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- 4. Find the general solution and the definite solution for the following differential equations: (a) +10y=15, y(0) = 0; (b) 2 + 4y = 6, y(0) =arrow_forward5. Find the solution to each of the following by using an appropriate formula developed in the lecture slides: (a) + 3y = 2, y(0) = 4; (b) dy - 7y = 7, y(0) = 7; (c) 3d+6y= 5, y(0) = 0arrow_forward1. Evaluate the following improper integrals: (a) fe-rt dt; (b) fert dt; (c) fi da dxarrow_forward
- 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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