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aw 4. Find when (r, s) = (1, -1) if w = (2+y+z)?, r=r-s, y = cos(r +s), z = sin(r +s). ar 5. Find the directional derivative of f(x, y, z) = 3x² + yz + 2yz? at P(1,1,1) in a direction normal to the surface x2 – y + z2 = 1.
2. Find the transfer functions Y(s)/R(s) of the following block diagram. (25 marks) R(s). G2G3 G G Y(s) 1 + G2G3H2 H/G₂h H
2. Find the closed loop transfer function, T(S)-Y(S)/R(S) by using Mason's rule. R(S) O 2
If z = f(x, y), where x = r + s and y=r – s, show that 2 2 дz Әх дz ду дz дz მr as
Consider the block diagram of the following control system. Find the transfer function G(s) = Y(S)/R(s) by using the block diagram reduction R(5) Y(s) + 5+2 s
Find the cardinality of the set {(r, y) E R? : x² + y? < 1}.
Problem 4: Find the transfer foRoor the llowing block diagram. Y (s) R(s) K1 F(s) G(s) K2
Find the transfer function Y(s)/R(s) in the given SFG. Use fx to input your answer. H2 Н. L L2 G2 G3 G4 R(S) Gs GS G6 G7 Y(S) L3 L4 Ho H7 Using SFG, find the transfer function C(s)/R(s). Use fx to input your answer here. R(S) C(s) X x G1 H1 H2 Find the transfer function C/R for the given SFG. Use fx to input your answer. G1 X1 G2 X2 R С -H Reduce into a single transfer...
3. Find the transfer functions for the following block diagram using block reduction 5 R(s) Y(s) G6
(i) Vz, y E R : (z +R y) , (z) +s (y) ii )-1s (5) A ring homomorphism. (2 pts) Let m be a positive integer, and let d be a positive divisor of Show that the map a : z/mZ 2/dZ by a(a mod m) show that t has properties (i)-(ii) in the previous problem mod d is a ring homomorphism (i.e.,