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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. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
Derivatives of Hyperbolic Functions : The last set of functions which we're going to be looking at is the hyperbolic functions. In several physical situations combinations of e
Find the common difference of an AP whose first term is 100 and sum of whose first 6 terms is 5 times the sum of next 6 terms. Ans: a = 100 APQ a 1 + a 2 + ....... a 6
20+20
When three quantities a, b and c are in G.P., then the geometric mean "b" is calculated as follows. Since these quantities are in G.P., the r
Determine whether the following numbers are odd or even: Examples: Determine whether the following numbers are odd or even: 364, 1068, & 257. Solution: 1.
What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication
Determine the value of a $1800 investment after six years at 9.3% per year, simple interest
briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived
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