(11) Show that the function is real when s is real, or when Re(s) -1/2.
11. Describe the branch cuts and branch points of the function (1-z2)1/2 and evaluate the real integral dx
11. Describe the branch cuts and branch points of the function (1-z2)1/2 and evaluate the real integral dx
Consider the function: 2) g(t) = tet"sin (et a)ls g(t) continuos at [0,°°] and of exponential order? b)Show that Laplace transform exist fot Re(s)>0
Consider the function: 2) g(t) = tet"sin (et a)ls g(t) continuos at [0,°°] and of exponential order? b)Show that Laplace transform exist fot Re(s)>0
Question 11 (2 marks) Attempt 2 rE[0,4] S is the surface2-16(y2+z2), DE[0,4]Obtained by rotating the function =4y about the x-axis for Given the vector field: E =(11y2-82)i+(132+12y) j+(12z-13y), Calculate the outward flux of E through surface S. That is find EdS S Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
Question 11 (2 marks) Attempt 2 rE[0,4] S...
DE Figure 11-1 Real GDP per hour worked, YIL Production function, Production function, Production function IC 18 1 $40 60 Capital per hour worked, KIL Refer to Figure 11-1. Diminishing marginal returns is illustrated in the per-worker production function in the ngure above by a movement from Production function to Production function 2 from Production function 2 to Production function 1 from Production function to Production function 3 up alone any of the production functions
Answer: 2 on 1 # 2 re The function g(x) = (x + 2 satisfies the hypotheses of the Mean Value Theorem (MVT) on the interval (-2,0). Find all number(s) X=C, -2 <c<0, that satisfy the conclusion of the MVT.
Consider the system with open-loop transfer function s+2 G(s) = k 82 4 Show the type of poles that the close-loop system has (real, imaginary, or repeated) for the different values ofk in [0 +00). Sketch the root locus of the close-loop system's poles when the gain k takes values in [0 +oo). Show clearly the break points of the loci, and calculate analytically the values that the branches of the loci are converging when k o
2. Use established properties of moduli to show that when |23| + |24|| Re(21 + z2) |z3 + z4| |z1| + |22|| - ||z3| – |z4|||
differential equations
(c) Let u = Re e +52+3+1. Show that u is harmonic function and find the harmonic conjugate v of u. [3]
Part 1. (Trigonometry - Complex Arithmetic - Linear Algebra) For any real number 0, let Re R2R be the linear transformation that is written in the standard basis as cosθ -sin θ sin cos 1.1. Draw a picture of the image of the unit square via R/s Describe the transformation in common words. 1.2. Compute det Re 1.3. Find (Re)-1 as a matrix. 1.4. Draw the image of the unit square via (R/s) How does this correspond to your description...
Y13) = re-1+21)22 42(2) = zel-1-21)22 Write the solution yı (2) as a sum of real and imaginary parts, y(I) = u(x) +iv(x), where u(2) and v(r) are real-valued. Based on the information given, are u(I) and v(2) solutions to the differential equation Briefly justify your answer.