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to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?
1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2
ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories Examp
Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to
Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y
PROBLEMS WITH APPLYING ALGORITHMS : From your experience, you would agree that children are expected to mechanically apply the algorithms for adding or subtracting numbers, regar
angel 1 and angel 2 are what angels?
Differentiate following. f ( x ) = sin (3x 2 + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.
Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require
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