
Find the minimum and the maximum values of
|z2 + (p + 1)i| on the closed disc {z ∈ C : |z| ≤ q + 1}
Find the minimum and the maximum values of 122 + (p + 1)i| on the closed disc {z € C: |Z| <q+1}.
8. This question has two parts. (i) Let G be a graph with minimum vertex degree 8(G) > k. Then prove that G has a path of length at least k. (ii) Let G be a graph of order n. If S(G) > nz?, then prove that G is connected.
need to solve using the 8 rules of inference
1.lv 2.-1 3. (-I v F) > () > M) 4.(MvH) > (S > 1) /S
mment 8.319 1) RCO,H 2) H,0 Draw the expected product(s). Consider whether a racemic mixture is expected, and if so, make sure to draw both enantiomers. Edit 8.31h 8.311
(1 point) Find the minimum and maximum of the function z-6x - 4y subject to 6x-3y 15 6x +y < 49 What are the corner points of the feasible set? The minimum is and maximum is . Type "None" in the blank provided if the quantity does not exist.
B. i) Convert ft) -10est+ 8est sin(12t) to the s-domain, for fit)>o. ii) Convert F(s) :24-to the time domain. s2+5s+6
2. Prove by induction that Ση.c)-(7+1) for n > 0 and i > 0.
For s > 0 define the gamma function I (s) by T () = [co-dt. Show that I (8) extends to an analytic function in the half-plane 20 = {ZEC: Rez >0}, and that the above formula continues to hold there. Hint: Show that S T. (s) ds = 0 for every triangle T in C where I (8) = le-+48-1dt for S E C and 0 <€ < 1.
How can I answer by maple
6. Consider the surface S described by r(u, ucos v, u sin v,1-2> (a) Graph the surface S for 0 u 2 and 0 (b) Identify the surface S thus obtained. u .
9. Prove by mathematical induction: -, i = 1 + 2 + 3+...+ n = n(n+1) for all n > 2.