Use Theorem 2.6.9∶Let p∈(0,∞).Then there is a unique x∈(0,∞),such that x^2=p
Problem:Prove that there is no n∈Z such that n^2=2
Use Theorem 2.6.9∶Let p∈(0,∞).Then there is a unique x∈(0,∞),such that x^2=p Problem:Prove that there is no...
a) Complete the statement of: Stoke's Theorem: Let S be an oriented surface bounded by a piecewise smooth simple closed curve with a positive orientation (i.e. clockwise relative to N). If F(x, y, z)=(M(x,y,z), N(x, y, z), P(x, y, z)) where M, N, and P have continuous partial derivatives in an open region containing Sand C, then: b) Use Stoke's theorem to write as an iterated integral, J. (y, -2', 1)odr where is the circle of radius 1 in the...
use divergence theorem Let S be the surface of the box given by {(x, y, z)| – 1 < x < 2, 05y<3, -2 << < 0} with outward orientation. Let F =< xln(xy), –2y, –zln(xy) > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SSĒ.ds S
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Let C be the triangle from (0, 0,0) to (2, 0, 0) to (0, 2, 1) to (0, 0, 0) which lies in the plane z 2 -Зугі + 4zj + 6x k, calculate | F . dr using Stokes's Theorem. If F(x, y, z) (b) 14 3 (c) 2 (d) 0 (e) None of these 10. Let C be the triangle from (0, 0,0) to (2,...
Please do 10 & 11 Use Intermediate Value Theorem lial p(x) = x4 +7x = 9 has two real root. 8. df Open with Google Docs Then use your calculator to find the ro 9 Let f(z)2with € [0, 00). Find a positive mumber e and two sequences {xn} and {yn} such that lim-(nn) = 0 but |f(xn)- f(Yn)| 2 e. Then conclude that f(x) = x2 is not uniformly continuous on [0, ao) [0, oo). Show that f is...
Discrete Structures Name: Problem 2. Prove the following theorem using P Theorem. Let x, y e Z. If c-y is odd, then 1 em using proof by contrapositive. yis odd, then ris odd or y is odd.
Finish the proof of Theorem 3.14. Theorem 3.14 Let (neN aand EneN be sequences in R. Let be in R# and suppose that x" → x, y, → oo, and z" →-oo. . If -oo <x o, then +yn 2. If-oo x < 00, then x" + Zn →-00 4. If-oo x < 0, then xoY" →-00 and xnZn → oo. 5. If x is in R. then-→0and-" →0 Proof Note that the conditions in the different parts of the...
4.8) a) Complete the statement of: The Divergence Theorem: Let D be a closed solid in space bounded by a closed surface s oriented by an outwardly directed unit normal vector n. If F(x, y, z)=(M(x,y,z), N(x, y, z), P(x, y, z)) where M, N, and P have continuous partial derivatives in D, then: D b) Use the Divergence Theorem to write as an iterated integral the flux of F=(x",x’y,x?:) over the closed cylindrical surface whose sides are defined by...
let a > 0 and define g(x) := x^(a+1) - (a+1)x + a. Use the mean value theorem to show that g(x)>0 for all x>0, where x~=1 3. Let α > 0 and define g(x):-Χα +1-(α + 1)x + α. Use the mean value theorem to show that (x>for allx >0, where x I 3. Let α > 0 and define g(x):-Χα +1-(α + 1)x + α. Use the mean value theorem to show that (x>for allx >0, where x...
Let X ~ N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = -1) = P(Z = 1) = 1/2) be independent of X. Let Y = ZX. What is the distribution of Y? Show that X and Y are uncorrelated. Are X and Y independent?
Let S be the surface of the box given by {(x, y, z) – 2 <<<0, -1<y<2, 0<z<3} with outward orientation. Let Ę =< -æln(yz), yln(yz), –22 > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SS F. ds S