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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 dierentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
A drug has a decay rate of k = - ¼ ln(¾) / hr. How soon after an initial dose of 1600 mg will the drug reach its minimum therapeutic value of 900 mg in the body?
If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans: AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A
f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
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A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F INSTRUCTIONS: Con
Venn Diagram - Set theory and calculus A easy way of representing sets and relations among sets is by means of the Venn diagram. Venn diagram includes of a rectangle that pres
Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia
scanning the demographic environment
A right triangular prism has volume equal to 288 cm^3. The height of the prism is 3 cm. One of the bases of the triangular face (not the hypotenuse) is equal to 12 cm, determine th
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