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Proper and Improper Fractions: Example: 3/8 proper fraction 8/3 improper fraction 3/3 improper fraction Here an improper fraction expressed as the sum of an in
Determine y′′ for x 2 + y 4 = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w
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
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
In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of
Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally
You plan to retire when you are 65th years old. You are now 25 years old. You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6
Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin
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
how to find equations of circles when given equations of centres on which it lies?
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