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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]
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli
The probability that a randomly selected 3-year old garter snake will live to be 4 years old is .54 (assume results are independent). What is the probability that five randomly se
Q) In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win
Q. Describe Laws of Cosines? The law of cosines is used to find the missing piece of a triangle if we are given either 1. Two sides and the included angle (SAS) or 2. All t
Proof of: lim q →0 sin q / q = 1 This proofs of given limit uses the Squeeze Theorem. Though, getting things set up to utilize the Squeeze Theorem can be a somewha
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
State DeMorgan's law. Prove it using the truth table. Ans: DeMorgan's law defines that (i) (x ∨ y)' = x' ∧ y' (ii) (x ∧ y)' = x' ∨ y' Now let us dr
If a pair of dice is thrown and X denotes the sum of the numbers on them. Find the probability distribution of X.Also find the expectation of X. SOLUTION: In a singl
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