Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 10, Problem 14P
Repeat problems P10-12 if
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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 10 Solutions
Introductory Mathematics for Engineering Applications
Ch. 10 - A faucet supplies fluid to a container of...Ch. 10 - The initial temperature of the hot coffee cup...Ch. 10 - A constant voltage vs(t)=10V is applied to the RC...Ch. 10 - Repeat parts (a)-(d) of the problem P10-3 if R=10k...Ch. 10 - Repeat parts (a)-(d) of the problem P10-3 if R=20k...Ch. 10 - A constant voltage vs(t)=10V is applied to the RC...Ch. 10 - Repeat problems P10-6 if R=200k and C=100F.Ch. 10 - Repeat problems P10-6 if R=100k, C=50F, vs(t)=20V...Ch. 10 - A sinusoidal voltage vs(t)=10sin(0.01t)V is...Ch. 10 - Repeat problem P10-9 if R=10k and C=10F.
Ch. 10 - Repeat problem P10-9 if R=20k and C=20F.Ch. 10 - The circuit shown in Fig. P10.12 consists of a...Ch. 10 - Repeat problems P10-12 if R=1k, C=10F, I=10mA, and...Ch. 10 - Repeat problems P10-12 if R=2k, C=100F, I=5mA, and...Ch. 10 - A constant current is(t)=100mA is applied to the...Ch. 10 - Repeat problems P10-15 if R=100 and L=100mH.Ch. 10 - Repeat problems P10-15 if R=100 and L=10mH.Ch. 10 - At time t=0, an input voltage vin is applied to...Ch. 10 - Repeat problems P10-18 if R=50 and L=500mH.Ch. 10 - Repeat problems P10-18 if R=10, L=200mH, and...Ch. 10 - The switch in the circuit shown in Fig. P10.21 has...Ch. 10 - A constant voltage source vin(t)=10 volts is...Ch. 10 - A sinusoidal voltage source vin(t)=10sin(10t)...Ch. 10 - The relationship between arterial blood flow and...Ch. 10 - Repeat problem P10-24 if the volumetric blood flow...Ch. 10 - The displacement y(t) of a spring-mass system...Ch. 10 - Repeat problem P10-26 if the displacement y(t) of...Ch. 10 - The displacement y(t) of a spring mass system...Ch. 10 - Repeat problem P10-28 if the displacement y(t) of...Ch. 10 - A block of mass m is dropped from a height h above...Ch. 10 - Repeat parts (a)-(c) of c problems P10-30 if...Ch. 10 - Repeat parts (a)-(c) of problems P10-30 if m=1kg,...Ch. 10 - The displacement y(t) of the spring-mass system...Ch. 10 - Under static loading by a weight of mass m, a rod...Ch. 10 - At time t=0, a cart of mass n moving at an initial...Ch. 10 - An LC circuit is subjected to a constant voltage...Ch. 10 - Repeat parts (a) and (b) of problem P10-36 if...Ch. 10 - An LC circuit is subjected to input voltage vin...Ch. 10 - Repeat parts (a)-(c) of problem P10-38 if L=100mH,...Ch. 10 - Repeat parts (a)-(c) of problem P10-38 if L=40mH,...Ch. 10 - Repeat parts (a)-(c) of problem P10-38 if L=40mH,...Ch. 10 - A biomedical engineer is designing a resistive...Ch. 10 - A rod of mass m and length l is pinned at the...
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