DISCRETE MATHS 8. Let 띠,22, , z,, be positive real numbers, and let ~ = (z,a2...

Question

Question

DISCRETE MATHS
8. Let 띠,22, , z,, be positive real numbers, and let ~ = (z,a2 xn)Un be their geometric mean. (For example, the geometric mea

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

let n be a positive integer and let x1,...,xn be real numbers. Prove that ( x1+...+xn)2...

let n be a positive integer and let x1,...,xn be real numbers. Prove that ( x1+...+xn)2 n(x12+ x22 +...+ xn2).
Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0...

Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0 0 an) be an n * n matrix, where a1, a2, . . . , an are nonzero real numbers. (a) Find the general solution to the system of equations -> -> x' = A * x (b) Solve the initial value problem x1(0) = x2(0) = · · · = xn(0) = k, for some constant k. (c) Solve the initial value problem (x1(0) x2(0)...
complex analysis Let f(z) be continuous on S where for some real numbers 0< a <...

complex analysis Let f(z) be continuous on S where for some real numbers 0< a < b. Define max(Re(z)Im(z and suppose f(z) dz = 0 S, for all r E (a, b). Prove or disprove that f(z) is holomorphic on S.

6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given a...

6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given arbitrary positive real numbers a and b, state a condition in terms of the fractional parts of and that is necessary and sufficient for la + bl = lal + Ibl Prove that this equation is true if and only if your condition holds. 7. Evaluate 10002+4 23k+5 k- 2 algebraically and simplify as much as possible. You ust show all steps....
5. Let {xn} and {yn} be sequences of real numbers such that x1 = 2 and...

5. Let {xn} and {yn} be sequences of real numbers such that x1 = 2 and y1 = 8 and for n = 1,2,3,··· x2nyn + xnyn2 x2n + yn2 xn+1 = x2 + y2 and yn+1 = x + y . nn nn (a) Prove that xn+1 − yn+1 = −(x3n − yn3 )(xn − yn) for all positive integers n. (xn +yn)(x2n +yn2) (b) Show that 0 < xn ≤ yn for all positive integers n. Hence, prove...
6. Let B(2) i + 22 4- 2iz (a) Find the smallest positive real value M...

6. Let B(2) i + 22 4- 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, B(2) <M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from -i to e3ri/4 and then bouncing from e3mi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we can obtain...

Problem 3. Let 21, 22, 23, 41, 42, y3 be some real numbers, and let A=...

Problem 3. Let 21, 22, 23, 41, 42, y3 be some real numbers, and let A= (1 12 13 (41 42 43); Prove (slowly) that dim (ker(A)) > 2 # dim (col(A)) <1 # dim (raw(A)) <1 + X1y2 = 91.22, x1y3 = y123, 22y3 = 42.23. Show that dim(col(A)) = dim(raw(A)) = 3 - dim(ker(A)).
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value...

Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value...

Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...

Problem 1 Let {ak} and {bk} be sequences of positive real numbers. Assume that lim “k...

Problem 1 Let {ak} and {bk} be sequences of positive real numbers. Assume that lim “k = 0. k+oo bk 1. Prove that if ) bk converges, so does 'ak k=1 k=1 2. If ) bk diverges, is it necessary that ) ak diverges? k=1 k=1