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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
1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by
If arg (a/b) = pi/2, then find the value of ((a+b)/(a-b)) where a,b are complex numbers. Ans) Arg (a/b) =Pi/2 Tan-1 (a/b)= Pi/2 A/B = tanP/2 ,therefore a/b=infinity.
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
If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro
Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul
find the unit rate. Round to the nearest hundredth in necessary 325 meters in 28 seconds
(4 sqrt3+5 sqrt2)/(sqrt48+ srt18)
The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and
(x+y+1)dy/dx=1
Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel
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