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Trace the curve y 2 = (x + 2) 2 (x - 6). Clearly state all the properties you have used for tracing it(e.g., symmetry about the axes, symmetry about the origin, points of interse
The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only
which ne is greater -4 4/25 or -4.12?
Example determines the first four derivatives for following. y = cos x Solution: Again, let's just do so
Consider the function f(x) = 2x 2 + 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use first principles.
(a) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by
If the roots of the equation (a-b) x 2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c. Ans: (a-b) x 2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B 2 - 4AC = 0
In a class, all pupils take Mathematics (M), 18 take Chemistry (C), 17 take Biology (B) and 24 take Physics (P) of those taking 3 subjects only, 5 take Physics and Chemistry, 7 ta
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
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
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