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17 Jun 2019: i) f(x) = ea|x|,. and (ii) g(x) ={. 1 , |x| 6 b0 , |x| > b. ... You may assume that (ab) = a.b b.a (b.)a (a.)b. ]. Show that, in a two-dimensional flow, vortex lines keep their strength and movewith the fluid.

17 Jun 2019: i) (A B) (B A) is finite and(ii) there is a finite set F A B such that f(x) = g(x) for all x A B F. ... c) Let p (0,1) and let a,b R with a < b.

17 Jun 2019: iv) Newton’s gravitational constant G;. (v) electric field E;. (vi) magnetic field B;. ... i) S1 = {f : A B | f is injective}.(ii) S2 = {g : B A | g is surjective}.(iii) S3 = {h : B B | h is bijective}.

17 Jun 2019: Deduce from (b) that if e is an eigenvector of D with eigenvalue. ... two solutions when there are infinitely many. Consider the case. A =. . . a a b. b a a. a b a.

17 Jun 2019: Use suffix notation to expand (a b) (b c).Let a, b, c be given unit vectors in R3, and let m = (a b) (b c) (c a). ... Show that f is continuous at x0. (b) State the Mean Value Theorem.

17 Jun 2019: Ḣ = 12M2Pl. φ̇2. (b) Consider the following ansatz for the scalar field evolution,. ... particle is at rest atthe origin at t = 0 and the magnetic field points in the positive z-direction with magnitude|B| = B.

22 Aug 2019: continuous? (b) Which of the following functions are uniformly continuous? Briefly justify youranswers. ... If themagnetic field is. B = b(x, y, 2z ) ,where b is a constant, find the induced current I, given that the total resistance of theloop is R.

16 Oct 2019: βxz〉CA |µxz〉B ,. where the 1-qubit states |µxz〉 are uniquely determined. ... P. . 0 1 0 0 a z. 1 c c a b b.

17 Jun 2019: table(Cases.of.flu). Hospital. Month A B C. April 10 40 27. ... b) Show that the above implies that an initially normalised probability distributionremains normalised,.

17 Jun 2019: Let b < min(a,r/C, 1/K). Show that there isa unique C1 function x : [b,b] [x0 r,x0 r] such that. ... a dr = 0,. L. (a r b dr b r a dr) = 0. ].