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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
solve x+y= 7 and x-y =21
Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second
Evaluate following sin 2 ?/3 and sin (-2 ?/3) Solution: The first evaluation in this part uses the angle 2 ?/3. It is not on our unit circle above, though notice that 2 ?/
what value of k is he sequence 2k+4,3k-7,k+12 are in an arithmetic sequence is
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School run known to possess normal distribution with mean 440 sec & SD 60 sec. What is probability that randomly chosen boy can run this race in 302 sec.
Explain Adding Rational Expressions with Different Denominators When you add or subtract fractions or rational expressions that have different denominators, you must first find
Evaluate the volume of a ball whose radius is 4 inches? Round to the nearest inch. (π = 3.14) a. 201 in 3 b. 268 in 3 c. 804 in 3 d. 33 in 3 b. The volume of a
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Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha
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