Please justify your answers : Which of the following sets are compact: i. {(z, y)E R...

Question

Question

Please justify your answers :

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

( { (any) EIR? n² ayes 1 The graph at the set is The shaded region is the set. so the set is not compact as it is not bounded

Answer 2

Similar Homework Help Questions

Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then...

Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 :...

(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
6. Justify briefly (max two lines) if the following statements are true or false. Answers with...

6. Justify briefly (max two lines) if the following statements are true or false. Answers with just Tor F won't receive any points. (a) (1 point) The curve with vector (Cartesian) equation r(t) = (t cost, tsint, t) lies on the surface with cylindrical equation 2 = 72 (b) (1 point) If ñ x p=0 then ñ = 0 or p=0. (c) (1 point) 24 – 4y2 lim (x,y)+(0,0) 22 + 2y2 = 0 (d) (1 point) If f(x, y)...

1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (...

1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that: 1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
(a) By the Heine-Borel Theorem, show that R2 is not compact and the sphere S2 ={(x,y,z)∈R3 :x2 +y2 +z2 =1} is compact in...

(a) By the Heine-Borel Theorem, show that R2 is not compact and the sphere S2 ={(x,y,z)∈R3 :x2 +y2 +z2 =1} is compact in R3. (b) Show that R2 and S2 is not homeomorphic. (i.e. no continuous bi- jective function f between R2 and S2 such that the inverse function f−1 is continuous). Question 1. (2 marks) (a) By the Heine-Borel Theorem, show that R2 is not compact and the sphere is compact in R3. (b) Show that R2 and S2...
in each case: (e) Compute y = sin(z)cos(r) for 0 < z < π/2

in each case: (e) Compute y = sin(z)cos(r) for 0 < z < π/2

Evaluate ∫∫∫ E √ x 2 + y 2 + z 2 d V where E...

Evaluate ∫∫∫ E √ x 2 + y 2 + z 2 d V where E lies above the cone z = √ x 2 + y 2 and between the spheres x 2 + y 2 + z 2 = 1 and x 2 + y 2 + z 2 = 9 . df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z =...

5 and 6 please 5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) r...

For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...

l. (Taylor Polynonial for cos(ar)) Fr f(z) = cos(ar) do the following. (a) Find the Taylor polynomials T.(r) about O fo...

l. (Taylor Polynonial for cos(ar)) Fr f(z) = cos(ar) do the following. (a) Find the Taylor polynomials T.(r) about O for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between T(r) and TR+1(r)? (c) You might want to approximate cs(ar) for all x in。Ś π/2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a-2, i.e. f(x)-cos(2x). d)...