(d) Sketch the image under the function f(z) Logz of the region (s : 비 > 1,0 etch the image unde...
5. Consider the function f(z)-1. (a) Sketch the horizontal line y 1/2 together with its image under f b) Verify that the image of line y- b>0 is a circle. What are its center and radius? c) What is the image of the half-plane : y>1/2 under f? 5. Consider the function f(z)-1. (a) Sketch the horizontal line y 1/2 together with its image under f b) Verify that the image of line y- b>0 is a circle. What are...
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working. (7) Let 0くa 〈 b 〈 c 〈...
Evaluate f(x, y, z) dV for the function f and region W specified. f(x, y, z) = ex + y + 2; W: 0 SX S 4,0 S Y S x, 0 sz s 2 eBook
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and 2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
2. Evaluate 1,(1,0, 2) . ds, where s is the cone z = VE4y2 with 0 < z < 2, Upward 1,0,2) ds, where S is the pointing normal. 3. Use a surface integral to find the area of the region of the plane z2y +3 with 2. Evaluate 1,(1,0, 2) . ds, where s is the cone z = VE4y2 with 0
(b) Determine the domain D of analyticity of the function f(z) = = Log(2 – į + 2), and find the derivative f'(2) on D.
Consider the function f and region E. f(x, y, z) = y, E = {(x, y, z)| 1 5 x2 +3? 59,0 SyS 1 - x2 - 22; (a) Express the region E in cylindrical coordinates. O E = {(r, 0, 2)Iisrs9,0 SO S 21,0 S 231-23 O E = {(1, 0, 2)| 1 575 3,0 SOST,O SZS 1-12} O E = {(r, 0, 2)Ii Srs 3,0 s E s 2,0 S 25 1 - 2 O E = {(r,...
2) Consider a random variable Z with a uniform probability density function given as UZ(-1,0) and X=4Z+4. a) Find and plot the probability density function ( ) Xf x . b) Find and plot the probability distribution function ( ) F x X . c) Find E[Z]. d) Find E[X]. e) Find the correlation of Z and X. i. Are they correlated? ii. Are they independent? Why? 2) Consider a random variable Z with a uniform probability density function given...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
5. Let S : R+Z be defined by f(x) = 11 (a) Sketch the graph of f. (b) Is f a one-to-one function? Justify your response.