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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
Find and classify the equilibrium solutions of the subsequent differential equation. y' = y 2 - y - 6 Solution The equilibrium solutions are to such differential equati
Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is
Give the introduction about Graphing? Somebody tells you that x = 5 and y = 3. "What does it all mean?!" you shout. Well here's a picture: This picture is what's call
(1) If the coefficient of friction between a box and the bed of a truck is m , What is the maximum acceleration with which the truck can climb a hill, making an angle q with the ho
Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
The length of the sides of a triangle are 2x + y/2 , 5 x/3 + y + 1/2 and 2/3 x + 2y + 5/2. If the triangle is equilateral. Find its perimeter. A ns: 2x + y/2 = 4x + y
A plane is illustrated by any three points that are in the plane. If a plane consists of the points P = (1, 0,0) , Q = (1,1,1) and R = (2, -1, 3) find out a vector that is orthogo
Midpoint Rule - Approximating Definite Integrals This is the rule which should be somewhat well-known to you. We will divide the interval [a,b] into n subintervals of equal wid
Definition of a Function Now we need to move into the second topic of this chapter. Before we do that however we must look a quick definition taken care of.
Chain Rule : We've seen many derivatives. However, they have all been functions similar to the following kinds of functions. R ( z ) = √z f (t ) = t 50
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