Practice Problem 3, (2 x 8 = 16 points (a) Whether is f(a)-Re() differentiable? Explain why (b) Check whether f()-Re(2)-Im(2) is an analytic function by checking the Cauchy- Riemann equations.
Suppose fis an entire function such that there is a number M such that Re(f(z)2 - Imf(z))2 s M for all z. Prove that f must bie Hint: Compare to exercises #8: if f and g are both entire, then so are f-g and gof. Find an appropriate g so that you may apply Liouville's theorem to the entire function gof
Let f(z) = ee^z . Find Re(f), Im(f) and |f|
Let f(x) (1/4) (1/2)for1,0,1 and f(x) a pmf? If yes, re-express the pmf by a table for other a values. Is f(x) r) 0 for oth er r values . Is f(x
Let f(x) (1/4) (1/2)for1,0,1 and f(x) a pmf? If yes, re-express the pmf by a table for other a values. Is f(x) r) 0 for oth er r values . Is f(x
Im In F 1 1 Re -6 -5 -4 -3 -2 -1 -it N 3 4 5 6 LL -6 -5 -4 -3 -2 Im Im ih -6-5-4-3-2 2 -it 5 Re 6 -6 -5 -4 -3 -1 -il Find the modulus r. o Graph the complex number. 2 + Si Im Im iF Re -6 -5 -4 -3 -2 -1 -i 1 2. 3 4 5 6 -6-5-4-3 -2 -1 -F 1 2 3 Im Im -6-5-4-3-2-1 - 1...
Suppose that UCC is open and connected and a E U. Let F:= {f € H(U)| Re(f)> 0, f(a) 1} Show that Fis normal.
Suppose that UCC is open and connected and a E U. Let F:= {f € H(U)| Re(f)> 0, f(a) 1} Show that Fis normal.
In Fig. 6.2-2, why does the f versus Re curve for turbulent
flow lie above the curve for laminar
flow rather than below?
1.0 0.5 0.2 0.1 Laminar 0.05 16 f= Re 0.02 Turbulent k/D 0.004 0.01 0.001 f 0.0791 Rel/4 0.0004 -0.0001 Hydraulically smooth" 0.005 0.002 10 106 105 0.001 102 103 104 Reynolds number Re D<ū> p/u Fig. 6.2-2. Friction factor for tube flow (see definition of f in Eqs. 6.1-2 and 6.1-3. ICurves of L. F. Moody,...
4. (5 points) (a): Find all second partial derivatives of f(x, y) = re-2ry, (b): Find dw/dt at t = 1 if w = re + y sin z - cosz, r= 2/t, y=t-1+ lnt, and 2 = t.
why H be normal subgroup of D6 in rapidly?
EIn F Re ED 4 HAK=SR. Rrfe 2D4)
EIn F Re ED 4 HAK=SR. Rrfe 2D4)
2. Suppose re - exeFereFeF, and ri - exFEDCBA98, find the result of the following operations (1) EOR r3, ri, re (2) ORR r3, r1, re (3) AND r3, rl, re (4) BIC r3, r1, re (5) BFI r3, r1, #4, #8 (6) MVN r3, r1 (7) MVN r3, re (8) MVN r3, re ADD r3, r1, r3
2. Suppose re - exeFereFeF, and ri - exFEDCBA98, find the result of the following operations (1) EOR r3, ri, re (2)...