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. Ether Simplidy or evaluate eh fellowin exprassis own Kpress.en 0 (t) a(st)
ſi, if 0 St<T, y" + 4y = 10, if a St< 0. y(0) = 0, y(0) = 0. 9
find laplace transform f(t) = {0, 0 st < 2 t2-1 t2 2 f(t) = {0, 0 st
Evaluate the following: where S-( (z, y) є R2 : 0 ST/2,0 < y ST/2). (a) Jls (cosz-s (b) fdl where y is the line segment from (2,-1,3) to (0, 1, 4) and f (x,y,z)-y+2 sin y) dA 3 marks 3 marks (c) Jc F dr where C is the unit circle centred at the origin, traversed once anticlockwise and F R2R2 is given by F(r,y)- (x2.x + y) 3 marks JJR eVEdA where R is the region enclosed by...
y'(0)= 0, y(0). = -1, 23. y"+ 4y g(t) where St. 15. t<2, g(t) t >2 y'(0)= 0, y(0). = -1, 23. y"+ 4y g(t) where St. 15. t2
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
Laplace transform of the unit step function y"+y= St/2, if 0 St<6, 13, if t > 6 y(0) = 6, y'(0) = 8
2. If C is the space curve given by F(t) = (t, t”, t') (0 St < 1) and F(x, y, z) = (1+z, cos(TX), e24), find ScF. dr.
8. (i) Find C[F(t)], where F(t) = { if 0 st 34, ift> 4 (ii) Compute the convolution e2 et directly by the definition of the convolution (iii) Evaluate Lle-2445 - e cos(4t) + sin(V2t)). blom.
5) Suppose that .02t if 0 <t< 2 St = .003t if 2 < t < 5 where t is in years. If an initial deposit of $150 when t = 0) is made (and no other deposits or withdrawals are made) then find how much is in the account at the end of the 5th year, and also find the equivalent effective annual interest rate for this 5 year period.
(2) 1-2 st 32 sec Given: xi(t) = {0 elsewhere and xz(t) = {o -2 st 32 sec elsewhere Use Fourier transform pairs/theorems to find the convolution z(t) = x1(t) * x2(t). Express your final answer in the time domain. (25 pts)