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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Determine and classify all the critical points of the given function. Described the intervals where function is increasing & decreasing. Solution: Firstly we'll require
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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
To find sq root by the simple step... root (-i)=a+ib............... and arg of -i= -pi/2 or 5pi/2
Tchebyshev Distance (Maximum Travel Distance per Trip Using Rectilinear Distance): It can be calculated by using following formula: d(X, Pi) = max{|x - ai|, |y - bi|} (Source
bunty and bubly go for jogging every morning. bunty goes around a square park of side 80m and bubly goes around a rectangular park with length 90m and breadth 60m.if they both take
Example Sketch the graph of following f( x ) = 2x and g( x ) = ( 1 /2) x Solution Let's firstly make a table of values for these two functions. Following is
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
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can u tell me a website for iit-jee questions?
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