Suppose f, g are two functions mapping positive real numbers to positive real numbers and f = O(g). Prove why each statement is true or false. (a) log2 f = O(log2 g) (b) √f = O(f) (c) fk + 100fk−1 = O(gk), for k ≥ 1
Let n be a positive integer and a,b,c be real numbers greater than 1. Select all of the statements that are true. In(a) In(b) = In for all ab > 1. (In(a)) = bin(a) In(a) = £In(a) In(a? +62)= 2ln(a) + 2in(b) In() - = In(a) - In(b) – In (c) s In(a-")= -nIn(a)
Suppose that 0 < a < b < c < d are Real numbers
(they are all positive and from smallest to greatest in
alphabetical order).
Order the following fractions from SMALLEST to LARGEST:
Suppose that 0 <a<b<c<d are Real numbers (they are all positive and from smallest to greatest in alphabetical order). Order the following fractions from SMALLEST to LARGEST: daba cbbc Choose the correct ordering from options below: O A. da a b C'b'c'b OB. a a d...
41. Let (an) be a sequence of strictly positive real numbers and Sn = ak (a) Suppose that the series Σ an/ S,. an is convergent, determine the nature of the series an is divergent, show that 00 (b) Suppose that the series 1 1 Sn-1 Sp an a/S Then deduce the nature of the series
41. Let (an) be a sequence of strictly positive real numbers and Sn = ak (a) Suppose that the series Σ an/ S,. an...
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
3. Let a, b, and c be real numbers, with c +0. Show that the equation ax2 + bx + c = 0 (a) has two (different) real solutions if 62 > 4ac, (b) has one real solution if 62 = 4ac, and (c) has two complex conjugate solutions if 62 < 4ac.
Let a, b, and c be three strictly positive real numbers. Two sub-intervals of the interval (0, a + b + c) are chosen at random. One of sub-intervals of length a, and the other of length b. Find the probability that the sub-intervals do not overlap (that is, that their intersection is empty).
QUESTION 1 Is the set of complex numbers {α i complex numbers? lal =r) where r is a real positive number a subfield of the field C of
QUESTION 1 Is the set of complex numbers {α i complex numbers? lal =r) where r is a real positive number a subfield of the field C of
Let a and b are two distinct real numbers. Show that if a < b, there exists irrational number c such that a < c < b.