GROUP WORK 1, SECTION 4.3 The Major Curve Pieces 1. What can we say about g.g,and g" for cach of these segments of the graph of y-g(x)? 245 GROUP WORK 1, SECTION 4.3 The Major Curve Pieces 1...
GROUP WORK 1, SECTION 14.3 Clarifying Clairaut's Theorem Consider f (x, y, z) = x?cos (y + 2). 1. Why do we know that fyyxxx=0 without doing any computation? 2. Do we also know, without doing any computation, that Sxyz = 0? Why or why not? 3. Suppose that a = 3x + ay". Jy = bxy + 2y. S,(1, 1) = 3, and has continuous mixed second partial derivatives xy and fyx. (a) Find values for a and b...
1. Say that we are attempting to evaluate sin ((x - 1)(y-2)) (x,y)+(1,2) (x - 1)2 + (y - 2)2 (a) Evaluate this limit as we approach the point (1,2) on the line x = 1. (b) Evaluate this limit as we approach the point (1,2) on the line y = 2. (c) From your work in (a) and (b), can you conclude that the limit above exists?
If the wage elasticity of labor supply is negative, what can we say about the slope of the labor supply curve and the relative sizes of the income and substitution effects? Is leisure a normal or inferior good in this case? Will a fall in the tax rate on earnings increase or decrease tax revenues?
Suppose a group G has order 35 and acts on a set S consist- ing of four elements. What can you say about the action? Hint: Must there be a fixed point?) b. 4. a. What happens if IGI-287 IGI-30? Suppose a group G has order 35 and acts on a set S consist- ing of four elements. What can you say about the action? Hint: Must there be a fixed point?) b. 4. a. What happens if IGI-287 IGI-30?
7 (a) What can you about the graph of a solution of the equation y' = xy' when x is close to 0? What if x is large? (b) Verify that all members of the family y = (c - x2)-1/2 are solutions of the differential equation y' = xy. (c) Find a solution of the initial value problem y' = xyº; y(0) = 2
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
The shape of a container is obtained by rotating the curve y = x^2 over the interval 0 ≤ x ≤ 2 about the y-axis. If the tank is full of water, the work required for pumping all water to the top of the tank can be expressed as an integral W = f(b,a) f(y)dy. Use trapezoidal rule on four subintervals of equal length to estimate the work. (Assume that water density is ρ kg/m3, and gravity acceleration g m/s2.)...
We were unable to transcribe this imageWe were unable to transcribe this imagec) Let y - Ara. Suppose that we see when p - 2 and w - 1 then x-3 and y-8. Also when p-1 and w 1.5, then x-4 and y - 10. Can we identify the parameters of the production function from these two observations? Graph what an economist who didn't know the functional form of the production function would conclude about the production set. c) Let...
Peer Leading Exercise 7 Spring 2019: Area Under the Given a function (x), the area under the curve is the area of the region bordered by the x -sxis and the graph of y(x). Area under the curve is somehow related to anti-derivatives. We wish to Example: Let f(x) -10-2x. Find the area under the curve between x 0 and x graph to help you visualize what is going on. Do you recognize the shape? 5. We include a 2...
Show all work please. 1. U(x, y) x,ax,1-a) a. Solve for the marshallian demands for x, and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). (4pts) b. For x, find the own-price elasticity and income elasticity. (4pts) c. Suppose a = d. What happens to these quantities when p1 doubles to $4? (4pts) e. What does this say about the price consumption curve (PCC)? (4pts) 100, p1 2, and p2=8, find the...