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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
824 divided by 4
The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first princ
how to find eigen value for the given matrix 122 021 -122
Three payments of $2000 (originally due six months ago, today, and six months from now) have been renegotiated to two payments: $3000 one month from now and a second payment due in
ABC is a right angled triangle in which ∠A = 900. Find the area of the shaded region if AB = 6 cm, BC=10cm & I is the centre of the Incircle of ?ABC. Ans: ∠A =90 0 BC
x+8/2=5x/6
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
seven more than a number is less than or equal to -18
Calculate average speed of a train: What is the average speed of a train which completes a 450-mile trip in 5 hours? Solution: Using Equation 15: V av = s/t V a
First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the
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