Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
Iff(z,y)-lth' if (z.v) * (0,0), cal late fy(0,0) andふ(0,0), and verify that are different. (This doesn't violate Clairaut's theorem because the partials are not continuous at the origin.). Hint: In class we showed that: a)(0.0) if (z,y) # (0,0) 0 if (z,y) = (0,0)
How to do the c and d?
Player 2 A-1,-1 0,0 0,0 0,0 5,5 Player 1 B 0,0 ci 0,0 0,0 Figure 2: A 3-by-3 Game (a) (2 points) First, what category of game does this fall into (e.g. prisoner's dilemma)? (b) (3 points) Next, find all of the Nash equilibria in this game, being careful to explain (c) (5 points) Which of the Nash equilibria is the best? Which is the worst? Justify Explain. the associated beliefs your answers...
Given the finite state machine: (c) 0,0 1,1 So Start S1 1,1 0,0 0,0 1,0 S2 S3 0,0 (i) Determine the transition table associated with the given state machine above (10/100) (ii) Write the simplest phrase structure grammar, G=(V,T,S,P), for the machine in 4(c)(i) (10/100) (iii Rewrite the grammar you found in 4(c)(ii) in BNF notation. (10/100) (iv) Determine the output for input string 1111, of the finite state machine in 4(c)i) (10/100)
Given the finite state machine: (c) 0,0...
(1 point) Consider the function defined by
?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2
except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0.
Then we have
∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)=
∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)=
Note that the answers are different. The existence and continuity
of all second partials in a region around a point guarantees the
equality of the two mixed second derivatives at the point. In the
above case, continuity fails at (0,0)(0,0).
(1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
Find a solution that is acceptable given the conditions that
u(0,0) = 6 and that ux(0,0) = 2
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f continuous at (0,0). 2. Compute the partial derivatives of f at any (x, y) E R2. Are the partial derivatives continuous (0,0). at (0,0) (0,0) and 3. Compute the second derivatives 4. Compute the linear approzimant of f at (0,0).
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f...
What is Va, Vb, and I?
For the circuit below, what is VA? 2001 | 1001 5v ) VA S VB 30022 3001
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
question number 5
(c) VA, va, V,) and V, VA, VB, and V,, only (d) 4. The current I in Figure 11-2 will change as the arm of the po- tentiometer is moved (a) True (b) False What advantage does the potentiometer method have over the fixed resistor method for voltage dividing? 5.