q1 Q.1, 2+2 pts] Sketch the domain of the following functions: (a) f(r, y)=Vry 4 25...
1. Sketch the domain of the following functions. (6 Pts) 12+y2 a) f(1,7) (b) g(x, y) = x2 + y2 - 4
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface.
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
Please help with the first two questions.
1. Sketch the domain of f(x,y) = 14 – x2 - y2 x-1 2. Sketch the domain of f(x,y) = In(y + x?) - -- y. 3. Find two level curves for f(x,y) = y - x + 1 (make sure to label k-values).
f(x, y) = sin '() - x?) 8. (6 pts) Find the domain of the following functions f(x, y) = Vor? + y2 – 25 1 f(x, y) = sin-'(y – x?)
Determine the domain of each of the functions P(x), Q(x), V(x), and Z(x). Select the one row that gives the correct domain underneath each function. P(x)= x2 + 1 Q(x) = Ne + 1 V(r) = **1 Z(x) = log (x + 1) OP: [-1, )Q: (-00, -1) (-1,00) V:(-0,0) Z: (-1,00) OP: (-00,00) Q: (-1,0) V: (-00, -1) (-1,0) Z: (-1,00) OP: (-00,00) Q: (-1,-) V: (-0, -1) U (-1,00) Z: (-1,0) OP: (-0, -1) U (-1,0) Q: (-1,-)...
1. Find the maxima of the following functions. (a) f(x)-2-4. )2 (c) f (z,y)2+3. (d) f (x,y) = xy-x2-y2 + 9y.
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
7) Let D be the domain described by -1 <y<1, x 2-1, r< y2 i) Sketch the domain D. neither? Is D horizontally simple, vertically simple, ii) Calculate the three integrals a = ffpxdxdy, b = SSpydxdy and iv) What physical meaning does the quantity What physical meaning does the point (a/c, b/c) have, related to the region D? or SSp drdy have, related to the region D? i) C= v) 5) The level curves of a function f(r,y) are...