A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 7, Problem 25RE
In Problems 25–28 use the unit step function to find an equation for each graph in terms of the function y = f(t), whose graph is given in Figure 7.R.1.
25. 
FIGURE 7.R.2 Graph for Problem 25
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Chapter 7 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1–18 use Definition 7.1.1 to find .
6....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....
Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - Prob. 22ECh. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - Prob. 28ECh. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - Prob. 38ECh. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - Prob. 40ECh. 7.1 - We have encountered the gamma function () in our...Ch. 7.1 - Prob. 42ECh. 7.1 - In Problems 4346 use Problems 41 and 42 and the...Ch. 7.1 - Prob. 44ECh. 7.1 - In Problems 4346 use Problems 41 and 42 and the...Ch. 7.1 - Prob. 46ECh. 7.1 - Suppose that if {f1(t)} = F1(s) for s c1 and that...Ch. 7.1 - Figure 7.1.4 suggests, but does not prove, that...Ch. 7.1 - Discussion Problems Use part (c) of Theorem 7.1.1...Ch. 7.1 - Under what conditions is a linear function f(x) =...Ch. 7.1 - Explain why the function f(t)={t,0t24,2t51/(t5),t5...Ch. 7.1 - Show that the function f(t)=1/t2 does not possess...Ch. 7.1 - The function f(t)=2tet2cost2 is not of exponential...Ch. 7.1 - If L{f(t)}=F(s) and a 0 is a constant, show that...Ch. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - In Problems 5558 use the given Laplace transform...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - The inverse forms of the results in Problem 49 in...Ch. 7.2 - The inverse forms of the results in Problem 49 in...Ch. 7.2 - In Problems 47 and 48 use one of the inverse...Ch. 7.2 - Prob. 48ECh. 7.2 - (a)With a slight change in notation the transform...Ch. 7.2 - Make up two functions f1 and f2 that have the same...Ch. 7.2 - Prob. 51ECh. 7.2 - Suppose f(t) is a function for which f (t) is...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - Find either F(s) or f (t), as indicated. {e2t(t ...Ch. 7.3 - Find either F(s) or f (t), as indicated. {et sin...Ch. 7.3 - Prob. 8ECh. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - In Problems 31 and 32 use the Laplace transform...Ch. 7.3 - In Problems 31 and 32 use the Laplace transform...Ch. 7.3 - A 4-pound weight stretches a spring 2 feet. The...Ch. 7.3 - Recall that the differential equation for the...Ch. 7.3 - Consider a battery of constant voltage E0 that...Ch. 7.3 - Use the Laplace transform to find the charge q(t)...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 4954 match the given graph with one of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - Prob. 62ECh. 7.3 - In Problems 6370 use the Laplace transform to...Ch. 7.3 - use the Laplace transform to solve the given...Ch. 7.3 - Prob. 65ECh. 7.3 - y + 4y = f(t), y(0) = 0, y(0) = 1, where...Ch. 7.3 - y + 4y = sin t U(t 2), y(0) = 1, y(0) = 0Ch. 7.3 - use the Laplace transform to solve the given...Ch. 7.3 - y + y = f(t), y(0) = 0, y(0) = 1, where...Ch. 7.3 - y+4y+3y=1U(t2)U(t4)+U(t6), y(0) = 0, y(0) = 0Ch. 7.3 - Suppose a 32-pound weight stretches a spring 2...Ch. 7.3 - Solve Problem 71 if the impressed force f(t) = sin...Ch. 7.3 - In Problems 73 and 74 use the Laplace transform to...Ch. 7.3 - In Problems 73 and 74 use the Laplace transform to...Ch. 7.3 - (a) Use the Laplace transform to find the current...Ch. 7.3 - (a) Use the Laplace transform to find the charge...Ch. 7.3 - A cantilever beam is embedded at its left end and...Ch. 7.3 - Solve Problem 77 when the load is given by...Ch. 7.3 - Find the deflection y(x) of a cantilever beam...Ch. 7.3 - A beam is embedded at its left end and simply...Ch. 7.3 - Discuss how you would fix up each of the following...Ch. 7.3 - Prob. 83ECh. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - Prob. 2ECh. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 15 and 16 use a graphing utility to...Ch. 7.4 - In Problems 15 and 16 use a graphing utility to...Ch. 7.4 - In some instances the Laplace transform can be...Ch. 7.4 - In some instances the Laplace transform can be...Ch. 7.4 - In Problems 1922 proceed as in Example 3 and find...Ch. 7.4 - In Problems 1922 proceed as in Example 3 and find...Ch. 7.4 - In Problems 1922 proceed as in Example 3 and find...Ch. 7.4 - In Problems 1922 proceed as in Example 3 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 3538 use (8) to evaluate the given...Ch. 7.4 - In Problems 3538 use (8) to evaluate the given...Ch. 7.4 - In Problems 3538 use (8) to evaluate the given...Ch. 7.4 - In Problems 3538 use (8) to evaluate the given...Ch. 7.4 - Use the Laplace transform and the results of...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 51 and 52 solve equation (10) subject...Ch. 7.4 - In Problems 51 and 52 solve equation (10) subject...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 59 and 60 solve equation (15) subject...Ch. 7.4 - In Problems 59 and 60 solve equation (15) subject...Ch. 7.4 - In Problems 61 and 62 solve the model for a driven...Ch. 7.4 - In Problems 61 and 62 solve the model for a driven...Ch. 7.4 - Discuss how Theorem 7.4.1 can be used to find...Ch. 7.4 - In Section 6.4 we saw that ty + y + ty = 0 is...Ch. 7.4 - (a)Laguerres differential equation ty+(1t)y+ny=0...Ch. 7.4 - The Laplace transform L{et2} exists, but without...Ch. 7.4 - Solve the integral equation f(t)=et+et0tef()d.Ch. 7.4 - (a) Show that the square wave function E(t) given...Ch. 7.4 - Use the Laplace transform as an aide in evaluating...Ch. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Appropriately modify the procedure of Problem 72...Ch. 7.4 - The charge q(t) on a capacitor in an LC-series...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - Prob. 10ECh. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - In Problems 13 and 14 use the Laplace transform to...Ch. 7.5 - In Problems 13 and 14 use the Laplace transform to...Ch. 7.5 - In Problems 15 and 16 a uniform beam of length L...Ch. 7.5 - In Problems 15 and 16 a uniform beam of length L...Ch. 7.5 - Someone tells you that the solutions of the two...Ch. 7.5 - Reread (i) in the Remarks at the end of this...Ch. 7.6 - In Problems 112 use the Laplace transform to solve...Ch. 7.6 - In Problems 112 use the Laplace transform to solve...Ch. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - In Problems 112 use the Laplace transform to solve...Ch. 7.6 - Prob. 6ECh. 7.6 - d2xdt2+xy=0d2ydt2+yx=0 x(0) = 0, x(0) = 2, y(0) =...Ch. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - In Problems 112 use the Laplace transform to solve...Ch. 7.6 - Prob. 13ECh. 7.6 - Derive the system of differential equations...Ch. 7.6 - (a) Show that the system of differential equations...Ch. 7.6 - (a) In Problem 12 in Exercises 3.3 you were asked...Ch. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - (a) Show that the system of differential equations...Ch. 7 - In Problems 1 and 2 use the definition of the...Ch. 7 - In Problems 1 and 2 use the definition of the...Ch. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - In Problems 324 fill in the blanks or answer true...Ch. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - In Problems 25–28 use the unit step function to...Ch. 7 - In Problems 2528 use the unit step function to...Ch. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - In Problems 29–32 express f in terms of unit step...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - In Problems 2932 express f in terms of unit step...Ch. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - In Problems 3542 use the Laplace transform to...Ch. 7 - Prob. 37RECh. 7 - In Problems 3542 use the Laplace transform to...Ch. 7 - y + 2y = f(t), y(0) = 1, where f(t) is given in...Ch. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - In Problems 3542 use the Laplace transform to...Ch. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - The current i(t) in an RC-series circuit can be...Ch. 7 - A series circuit contains an inductor, a resistor,...Ch. 7 - A uniform cantilever beam of length L is embedded...Ch. 7 - When a uniform beam is supported by an elastic...Ch. 7 - Suppose two identical pendulums are coupled by...Ch. 7 - Coulomb Friction Revlslted In Problem 27 in...Ch. 7 - Range of a ProjectileNo Air Resistance (a) A...
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- d₁ ≥ ≥ dn ≥ 0 with di even. di≤k(k − 1) + + min{k, di} vi=k+1 T2.5: Let d1, d2,...,d be integers such that n - 1 Prove the equivalence of the Erdos-Gallai conditions: for each k = 1, 2, ………, n and the Edge-Count Criterion: Σier di + Σjeл(n − 1 − d;) ≥ |I||J| for all I, JC [n] with In J = 0.arrow_forwardT2.4: Let d₁arrow_forwardSolve the following boundary value problem using method of separation of variables: 1 ə ди r dr 70% (107) + 1 д²и = 0, 12802 -πarrow_forwardT2.3: Prove that there exists a connected graph with degrees d₁ ≥ d₂ >> dn if and only if d1, d2,..., dn is graphic, d ≥ 1 and di≥2n2. That is, some graph having degree sequence with these conditions is connected. Hint - Do not attempt to directly prove this using Erdos-Gallai conditions. Instead work with a realization and show that 2-switches can be used to make a connected graph with the same degree sequence. Facts that can be useful: a component (i.e., connected) with n₁ vertices and at least n₁ edges has a cycle. Note also that a 2-switch using edges from different components of a forest will not necessarily reduce the number of components. Make sure that you justify that your proof has a 2-switch that does decrease the number of components.arrow_forwardT2.2 Prove that a sequence s d₁, d₂,..., dn with n ≥ 3 of integers with 1≤d; ≤ n − 1 is the degree sequence of a connected unicyclic graph (i.e., with exactly one cycle) of order n if and only if at most n-3 terms of s are 1 and Σ di = 2n. (i) Prove it by induction along the lines of the inductive proof for trees. There will be a special case to handle when no d₂ = 1. (ii) Prove it by making use of the caterpillar construction. You may use the fact that adding an edge between 2 non-adjacent vertices of a tree creates a unicylic graph.arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward= == T2.1: Prove that the necessary conditions for a degree sequence of a tree are sufficient by showing that if di 2n-2 there is a caterpillar with these degrees. Start the construction as follows: if d1, d2,...,d2 and d++1 = d = 1 construct a path v1, v2, ..., vt and add d; - 2 pendent edges to v, for j = 2,3,..., t₁, d₁ - 1 to v₁ and d₁ - 1 to v₁. Show that this construction results vj in a caterpillar with degrees d1, d2, ..., dnarrow_forwardDo the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward12. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.508.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x + 16 dx X Need Help? Read It SUBMIT ANSWER 13. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.512.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx 8)(2x + 1) Need Help? Read It SUBMIT ANSWER 14. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.518.XP. Find the area of the region under the given curve from 1 to 5. y = x² +7 6x - x² Need Help? Read It ASK YOUR TEAarrow_forwardLakshmi planted 20 begonias, but her neighbor’s dog ate 7 of them. What percent of the begonias did the dog eat?arrow_forwardDETAILS MY NOTES SESSCALCET2 6.3.012. 6. [-/1 Points] Evaluate the integral. x-4 dx x² - 5x + 6 Need Help? Read It SUBMIT ANSWER 7. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.019. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x²+1 (x-6)(x-5)² dx Need Help? Read It SUBMIT ANSWER 8. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.021. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ✓ x² 4 +4 dxarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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