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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
2cos^2x-sinx=1......Find x
Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT
Example of Implicit differentiation So, now it's time to do our first problem where implicit differentiation is required, unlike the first example where we could actually avoid
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
As we saw in the previous section computing Laplace transforms directly can be quite complex. Generally we just utilize a table of transforms when actually calculating Laplace tran
Eliminate the parameter from the subsequent set of parametric equations. X = t 2 + t Y = 2t - 1 Solution: One of the very easy ways to eliminate the parameter is to
ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans: ΔAPR ∼ Δ
The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equivalent the lesser. What is the value of the lesser integer? Let x =
sin30+cos30=
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