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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
There are k baskets and n balls. The balls are put into the baskets randomly. If k
) Show that the following argument is valid: (~p ? q) => r s ? ~q ~t p => t (~p ? r) => ~s ------------------------ ? ~q 2) Show that the following argum
5 2 --- - --- x-1 x+1
If 3x2 is multiplied by the quantity 2x3y raised to the fourth power, what would this expression simplify to? The statement in the question would translate to 3x 2 (2x 3 y) 4 .
It's now time to do solving systems of differential equations. We've noticed that solutions to the system, x?' = A x? It will be the form of, x? = ?h e l t Here l and
Calculus Calculus is a branch of mathematics which describes how one variable changes in relationship to another variable. It enables us to determine the rate of change of one
Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to
Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several
Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the
how do you do it
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