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Equation of line joining(0,0)and point of intersection of X2+Y2+2XY=4 , 3x2+5y2-xy=7 is solution) The two equations above represent pair of straight lines. We can complete the square and arrive at the 4 line equatons and find their point of intersecrtion.Simple method (by mere observation) we can say X=1&Y=1 satisfies both the equation.therfore, Line passing through origin and (1,1) is :X=Y.=>X=Y is the reqd line equation
Theorem Consider the subsequent IVP. y′ = p (t ) y = g (t ) y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i
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what are eigen values
The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin
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 compl
Find out some solutions to y′′ - 9 y = 0 Solution We can find some solutions here simply through inspection. We require functions whose second derivative is 9 times the
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Define tautology and contradiction. Ans: If a compound proposition comprises two atomic propositions as components, after that the truth table for the compound proposition con
Multiplication of complex numbers After that, let's take a look at multiplication. Again, along with one small difference, it's possibly easiest to just think of the complex n
Newton's Method : If x n is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x n ) ≠ 0 the next approximation is given by
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