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Q: Find k, given f(x, y) = k(y² + xy) and [ [ f(x, y) dxdy = 54 R R=0 < x < y < 2
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Do question 33.
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- Evaluate _i(z³+i° 3³ +₁³) 2 z +1find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0, 0, 0) 2. 7(2, x, x^2)-5(2 -x, x^2) = (1, 12x, x^2)+3(1, 0, 1) 3. (sin x, sin2x, lne) = (sinπ, 2sinx, secx) cosx 4.for the given vectors find the value of U V ad normalise U+V U =(1, 1, 3) V = (3, 1, 1)Chapter 13, Section 13.6, Question 001 Find Duf at P. 1 1 3/2 f (x, y) = 3(1+ xy)2; P (1,3); u = i+ j Enter the exact answer. Duf = ? Edit
- Find the domain and rang x+Z+ 3 Siny of f(x.y,2) X+광-2Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to distribute (a + b) (c + d) yields )= (cos u) ( cos v) – (sin u) (sin e) cos u + i sin u Cos v + i sin v COS [(- (cos u) (sin v) + (sin u) (cos v) + i COS 1 Rewrite the right-hand side of the above identity using addition formulas : { (cos u) ( cos v) (- sin u) (sin v) co« (u + v). COs u %3D COS (cos u) (sin v) + (sin u) (cos v) sin (u + v) . COS Answer u + v + i sin COSFind all the roots of z²= - 1+ /3j A z=V2 (cos (-+ka) +j sin(-+ka)),k=-1,0 3 元 B =V2 (cos (-+kx) +j sin (- + ka)), k=0, 1 В C z=2 (cos -+j sin-) 3 3. D) z=V2 (cos (-+kx)+/ sin (+kr)), k=0, 1 12 + ka)), k=0, I 12
- f(csc x cot x + 3x2)dx csc x – x3 + c csc x + x3 + c - csc x + x3 +c .3 x° + c O cotx + x3+cHow do I parametrize to get r1(x) and r2(x).A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) Determine the coordinates of the particle if it travelled 10 units from (cos(4), sin(4),2)
- A particular solution of y" + y = sinx + xcosx -(x²sinx – 2xcosx) 4 a. b. (x?sinx – xcosx) 4 (x?sinx + xcosx) C. (x?sinx - 2xcosx) d. 글 2x3sinx-xcosx) е.Verify that sin(x+y)+sin(x-y)=2sinxcosy2. Prove that B(m,n) = B(m + 1, n) + B(m,n + 1) (10 marks) 3. Evaluate /= (1 +x)P x) dx in terms of p and q then find I if Assume Y - cos2A) (20 morke)