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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
Euler's Method Up to this point practically all differential equations which we've been presented along with could be solved. The problem along with this is which the exceptio
Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning: Assume that n 2 is
First, larger the number (ignoring any minus signs) the steeper the line. Thus, we can use the slope to tell us something regarding just how steep a line is. Next, if the slope
x>4
Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.
Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r
what are the advantages and disadvantages of tchebycheffs inequality theorem
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Larry purchased 3 pairs of pants for $24 each or have 5 shirts for $18 each. How much did Larry spend? Divide the miles through the time to find the rate; 3,060 ÷ 5 = 612 mph.
maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0
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