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Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)
7th Edition
ISBN: 9780137394524
Author: R. Nagle, Edward Saff
Publisher: PEARSON+
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Textbook Question
Chapter 3.2, Problem 9E
In 1990 the Department of Natural Resources released 1000 splake (a crossbreed of fish) into a lake. In 1997 the population of splake in the lake was estimated to be 3000. Using the Malthusian law for population growth, estimate the population of splake in the lake in the year 2020.
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(^)
k
Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as
n!
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Question 1.
(1) Prove the following identity: (22) + (1121) = (n+1).
(2) Use the identity above to prove the binomial theorem by induction. That
is, prove that for any a, b = R,
n
(a + b)" = Σ (^)
an-
n-kyk.
k=0
n
Recall that Σ0 x is short hand notation for the expression x0+x1+
+xn-
(3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using
the binomial theorem.
-
Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y.
Question 3. Assume (In) nEN is a sequence which is unbounded above. That is,
the set {xn|nЄN} is unbounded above. Prove that there are natural numbers
N] k for all k Є N.
be natural numbers (nk Є N). Prove that
Question content area top
Part 1
Find the measure of
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for the congruent triangles ABC and
Upper A prime Upper B prime Upper C primeA′B′C′.
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1533
2930
Part 1
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ABCequals=enter your response heredegrees
Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways 
Chapter 3 Solutions
Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)
Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A swimming pool whose volume is 10,000gal contains...Ch. 3.2 - The air in a small room 12ft by 8ft by 8ft is 3...Ch. 3.2 - Beginning at time t=0, fresh water is pumped at...Ch. 3.2 - A tank initially contains S0lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Prob. 10E
Ch. 3.2 - Prob. 11ECh. 3.2 - For the logistic curve15, assume pa:=p(ta) and...Ch. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - 16 Show that for a differentiable function p(t),...Ch. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - A snowball melts in such a way that the rate of...Ch. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - During the summer the temperature inside a van...Ch. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 7ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 9ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - In Problem 16, let I=50 kg-m2 and the retarding...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Rocket Flight. A model rocket having initial mass...Ch. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - An RL circuit with a 5- resistor and a 0.05-H...Ch. 3.5 - Prob. 2ECh. 3.5 - The pathway for a binary electrical signal between...Ch. 3.5 - If the resistance in the RL circuit of Figure...Ch. 3.5 - Prob. 5ECh. 3.5 - 6. Derive a power balance equation for the RL and...Ch. 3.5 - 7. An industrial electromagnet can be modeled as...Ch. 3.5 - 8. A 108F capacitor 10 nanofarads is charged to 50...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - In Example 1, page 126, the improved Eulers method...Ch. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Use the improved Eulers method subroutine with...Ch. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Use the improved Eulers method with tolerance to...Ch. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - The solution to the initial value problem...Ch. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 20ECh. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - The Taylor method of order 2 can be used to...Ch. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21E
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