Exercise 4 Leta(c)-c1/2 and let c2 > cı > 0 be given. Let: π1c1+12c2. where π2 = 1-T1. (i) Sketch the function u and indicate in your sketch the points (C1, u(a), (c, u(c)), and (c2,u(c2)). (ii) Draw the line that connects the two points (ci, u(cı)) and (c2, u(c2)) and represent that line algebraically. Hint: Find the slope and intercept in terms of the two points, (c1, u(c) and (c,,u (сг)).] (iii) Use that algebraic result to show that...
Let R be the region shown above bounded by the curve C = C1[C2.
C1 is a semicircle with center
at the origin O and radius 9
5 . C2 is part of an ellipse with center at (4; 0), horizontal
semi-axis
a = 5 and vertical semi-axis b = 3.
Thanks a lot for your help:)
1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
(4) Let f R -R be a strictly conve:r C2 function and let 0 a) Write the Euler-Lagrange equation for the minimizer u.(x) of the following problem: minimize u subject to: u E A, where A- 0,REC1[0 , 1and u (0 a u(1)b) b) Assuming the minimizer u(a) is a C2 function, prove t is strictly convex
(4) Let f R -R be a strictly conve:r C2 function and let 0
a) Write the Euler-Lagrange equation for the minimizer u.(x)...
find the eigen space of 4a and 4c
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6.
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
Question 4 (1 point) Let the sample data be: C1 C2 c3 1 0 2 2 1 1 3 1 1 1 3 2 2 2 1 3 2 1 3 1 3 2 2 3 1 1 3 1 P (C1 ? 3, C2 1, C3 2| O 0)= 1/64 1/8 1/27 1/32 Question 5 (1 point) Let the sample data be:
4/ Let α and β be the roots of ax2 + bx + c--0. Show that the equation whose roots are (α + β)2 and
PLS show your work 4. Let / be an entire function on C such that 11 (2) ► as 17| → . Prove that there exists a point zo in C for which /(20) = 0.
Let C be the curve parameterized by with 0 ≤ t ≤ 2π.
a) Show that the curve C is contained in a plane and that it is
a closed curve. You must explicitly give the equation of the plane
that contains the curve.
*( Reminder: the general equation of a plane is ax + by + cz =
d.)
b)Let P be the plane found in a). Calculate the area of the part
of P delimited by curve C...
The diagram below is for C. 2p C 1 C2 p 0 2i C 1 2s C 2 21-0 11. The bond order of the ground state is 12. C would be(more or less) stable than ground state C 13. Label the orbital marked above Below is the molecular orbital diagram for LiF 4 0 2s located on F 2s
The diagram below is for C. 2p C 1 C2 p 0 2i C 1 2s C 2 21-0 11....
Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the classifaction theorem
Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the...