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Proof of: if f(x) > g(x) for a x b then a ∫ b f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop
x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.
Calculate the introduction to Probability? Probability refers to the chance that an event will happen. Probability is presented as the ratio of the number of ways an event can
Power Series and Functions We opened the previous section by saying that we were going to start thinking about applications of series and after that promptly spent the section
Assumptions The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The
Using Substitution Solving Polynomial Equations ? Solve : (x 3 + 4) 2 - 15 (x 3 + 4) + 36 = 0. You might be tempted to multiply everything out and factor. However, there
Standardization of Variables - Before we use the general distribution curve to determine probabilities of the continuous variables, we require standardizing the original units
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
Work : It is the last application of integral which we'll be looking at under this course. In this section we'll be looking at the amount of work which is done through a forc
We'll include this section with the definition of the radical. If n is a +ve integer that is greater than one and a is a real number then, Where n is termed as the index,
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