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6. Let f(x,y) = xy+sin(x). Find all directions (unit vectors) so that the directional derivative off...
S (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P ...
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
2. Let f(x,y) == xy + sin(x). Find a unit vector ū such that for the...
2. Let f(x,y) == xy + sin(x). Find a unit vector ū such that for the directional derivative Daf(7,0) one has Daf(1,0) = -_. 27+127. b. None of the other alternatives is correct. Ocū7-7
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 +...
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 + z2 + 5 at the point (1, -3,2) in the direction of the vector < 1,0,-1>. (Hint: Use the results of partial derivatives from part(a))
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
3. Let f(,y) = cos(xy) and a =(,1). (a) Find f(a). (b) Find a unit vector...
3. Let f(,y) = cos(xy) and a =(,1). (a) Find f(a). (b) Find a unit vector which is normal to the level set {(x,y): f(x,y) = 0} at the point a. (c) For the unit vector ū= (-3), find the directional derivative Daf(a). (d) What is the largest possible value for Duf(a) among all unit vectors ü? What is the least possible value? (e) Consider the path elt) = (1,7)+(-), and the composition g(t) = f oct). Find g(0).
Question 5 Find the directional derivative off at P in the direction of a. f(x, y,...
Question 5 Find the directional derivative off at P in the direction of a. f(x, y, z) = xy +z+; P(2, -2,2); a =i+j+k Duf = ? Edit
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy +...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy +...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. 2) The direction in which f decreases most rapidly at A(0,1,1) is: 2 a. + 3 b. 是最+ i ++ d. 高+ C. 3 14 e. None of the above
D a) Fint oflay) f (x, y) = x² + sin(xy) for the function b) find...
D a) Fint oflay) f (x, y) = x² + sin(xy) for the function b) find the derivative flxigt & + sinkry) in the direction ů=chiss at the point (1,0)
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
2. Let f(x,y) == xy + sin(x). Find a unit vector ū such that for the directional derivative Daf(7,0) one has Daf(1,0) = -_. 27+127. b. None of the other alternatives is correct. Ocū7-7
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 + z2 + 5 at the point (1, -3,2) in the direction of the vector < 1,0,-1>. (Hint: Use the results of partial derivatives from part(a))
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
3. Let f(,y) = cos(xy) and a =(,1). (a) Find f(a). (b) Find a unit vector which is normal to the level set {(x,y): f(x,y) = 0} at the point a. (c) For the unit vector ū= (-3), find the directional derivative Daf(a). (d) What is the largest possible value for Duf(a) among all unit vectors ü? What is the least possible value? (e) Consider the path elt) = (1,7)+(-), and the composition g(t) = f oct). Find g(0).
Question 5 Find the directional derivative off at P in the direction of a. f(x, y, z) = xy +z+; P(2, -2,2); a =i+j+k Duf = ? Edit
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. 2) The direction in which f decreases most rapidly at A(0,1,1) is: 2 a. + 3 b. 是最+ i ++ d. 高+ C. 3 14 e. None of the above
D a) Fint oflay) f (x, y) = x² + sin(xy) for the function b) find the derivative flxigt & + sinkry) in the direction ů=chiss at the point (1,0)
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