(k+1) ==|r(t − t) = R(t)|. The integration may be continued until a threshold of (+1) (k) < 10-7 is reached.

Draw by hand the Bode plot of the following systems. 1. 50 G(s) : s(s² + 4s + 8) 2. 20(s + 1) s(s² + 2s + 10)(s + 5) G(s) =

Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f(x, y) = 9 sin(x) sin(y),   −? < x < ?,   −? < y < ? local maximum value(s)       local minimum value(s)       saddle point(s) (x, y) =

Solve the initial value problem. y" + 4y' + 20y = 0: y(0) = 2 y (0) = - 3 %3D Chapter 6, Section 6.2, Go Tutorial Problem 12 Find Y(s). 2s + 5 Y(s): s2 + 4s + 20 2s + 5 Y(s) = s2 + 4s + 20 2s – 5 Y(s) : + 4s + 20 2 + 4s + 20 Y(s) 2s + 5

(3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z epis

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11- If A, B and C are three mutually exclusive events in the sample space then P(AUB UC) = a- P(A)+P(B) + P(C) b- P(A) + P(B)+P(C) c- P(A) + P(B)+P(C)-P(ABC) d- P(A)+P(B)

M O :1 Find the limit for the following lim sin(3y).cot (5y) y.cot (4y) اجابتك Plot the following function y=cos((2n/5)-x) اجابتك Evaluate the following logV10 x logvz x اجابتك

F= 7 K = 6

Example 1: Expand the following by PF s (s+1)(s+2)