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The graph Cn, n ≥ 3 contains n vertices and n edges creating a cycle. For what value of n is Cn a bipartite graph? Draw the bipartite graph of Cn to give explanation for your answer.
Ans: For n = 2k, k = 2, 3, 4, ..., Cn is a bipartite graph. C6 that is drawn below which is bipartite graph.
1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even. 2.Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2. 3.let r>0 an
Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1 d (a x ) /dx= a
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If y 1 (t) and y 2 (t) are two solutions to y′′ + p (t ) y′ + q (t ) y = 0 So the Wronskian of the two solutions is, W(y 1 ,y 2 )(t) = =
Differentiate following functions. Solution At this point there in fact isn't a lot of cause to use the product rule. We will utilize the product rule. As we add
Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
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