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ei0 : 0 E R} be the group of all complex numbers on the unit circle...
Only need answer from (IV) to (VI) Only need answer from (IV) to (VI) Math 3140...
Only need answer from (IV) to (VI)
Only need answer from (IV) to (VI)
Math 3140 page 1 of 7 1. (30) Let R be the group of real numbers under addition, and let U = {e® : 0 E R} be the group of all complex numbers on the unit circle under multiplication. Let o: R U be the map given by = e is a homomorphism of groups. (i) Prove that (i) Find the kernel of . (Don't...
Let U be an open subset of R". Let f: UCR" ->Rm. (a) Prove that f...
Let U be an open subset of R". Let f: UCR" ->Rm. (a) Prove that f is continuously differentiable if and only if for each a e U, for eache > 0, there exists o > 0 such that for each xe U, if ||x - a| << ô, then |Df (x) Df(a)| < e.
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following:...
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
A weird vector space. Consider the set R+ = {x ER : x > 0} =...
A weird vector space. Consider the set R+ = {x ER : x > 0} = V. We define addition by x y = xy, the product of x and y. We use the field F = R, and define multiplication by co x = xº. Prove that (V, O, RO) is a vector space.
PROVE: 4. If f : R → R is a strictly increasing function, f(0) = 0,...
PROVE:
4. If f : R → R is a strictly increasing function, f(0) = 0, a > 0 and b > 0, then
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that
2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area...
2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area σ1 sitting at the origin. There is also an infinie plane parallel to the x- y plane sitting at z-zo with charge per unit area Oz. We will take Zo > R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo,0,0) with xo> R 2.3 15 POINTS The point (X1, 0,21) with 0 <...
Let Xi X, lid f(r 0) with f(r:0)-e ( e) for r > ? and ?...
Let Xi X, lid f(r 0) with f(r:0)-e ( e) for r > ? and ? e R. (a) Find the MLE of ? (c) Using the prior density ?(0)-e-91(0,0)( ?), find the Bayesian estimator of ?
Please prove this, thanks! 2. Let {xn n21 be a sequence in R such that all...
Please prove this, thanks!
2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M...
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M > M is a TM and 1011 E L(M)}.
Only need answer from (IV) to (VI)
Only need answer from (IV) to (VI)
Math 3140 page 1 of 7 1. (30) Let R be the group of real numbers under addition, and let U = {e® : 0 E R} be the group of all complex numbers on the unit circle under multiplication. Let o: R U be the map given by = e is a homomorphism of groups. (i) Prove that (i) Find the kernel of . (Don't...
Let U be an open subset of R". Let f: UCR" ->Rm. (a) Prove that f is continuously differentiable if and only if for each a e U, for eache > 0, there exists o > 0 such that for each xe U, if ||x - a| << ô, then |Df (x) Df(a)| < e.
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
A weird vector space. Consider the set R+ = {x ER : x > 0} = V. We define addition by x y = xy, the product of x and y. We use the field F = R, and define multiplication by co x = xº. Prove that (V, O, RO) is a vector space.
PROVE:
4. If f : R → R is a strictly increasing function, f(0) = 0, a > 0 and b > 0, then
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that
2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area σ1 sitting at the origin. There is also an infinie plane parallel to the x- y plane sitting at z-zo with charge per unit area Oz. We will take Zo > R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo,0,0) with xo> R 2.3 15 POINTS The point (X1, 0,21) with 0 <...
Let Xi X, lid f(r 0) with f(r:0)-e ( e) for r > ? and ? e R. (a) Find the MLE of ? (c) Using the prior density ?(0)-e-91(0,0)( ?), find the Bayesian estimator of ?
Please prove this, thanks!
2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M > M is a TM and 1011 E L(M)}.
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