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Problem #7: The graph of z =f(x,y) is shown below. In each part, determine whether the given part...
Problem #7: The graph of z = f (x, y) is shown below. In each part,...
Problem #7:
The graph of z = f (x, y)
is shown below. In each part, determine whether the given partial
derivatives are positive, negative, or zero. (Note that the
function is symmetric about 0 in both the x- and
y- directions.)
(a)
fx(−2, 2) and
fxx(−2, 2)
(b)
fy(−2, 2) and
fyy(−2, 2)
(c)
fx(0, −2) and
fxx(0, −2)
(d)
fy(0, −2) and
fyy(0, −2)
(A) negative, positive (B) negative, zero (C)
positive, negative (D) positive, zero (E) zero, ...
The graph of z = f (x, y) is shown below. In each part, determine whether the given partial derivatives are positive, negative, or zero. (Note that the function is symmetric about 0 in both the x- and y- directions.)
Problem #7:The graph of z = f (x, y) is shown below. In each part, determine whether the given partial derivatives are positive, negative, or zero. (Note that the function is symmetric about 0 in both the x- and y- directions.)(a) fx(2, 2) and fxx(2, 2)(b) fy(2, 2) and fyy(2, 2)(c) fx(−2, 0) and fxx(−2, 0)(d) fy(−2, 0) and fyy(−2, 0)(A) zero, positive (B) negative, negative (C) negative, zero (D) zero, negative (E) positive, negative (F) zero, zero (G) positive, positive (H) positive, zero (I) negative, positive Problem...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x +...
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
5. Given the graph of y = f(x), shown below, answer the following, by inspection. (0.5...
5. Given the graph of y = f(x), shown below, answer the following, by inspection. (0.5 mark each, 4.5 marks total). 2 2 -3 -6 -7 a) f(0) = b) f(2)= c) lim f(x) = d) lim f(x) = e) lim, f(x) = d) lim f(x) = g) lim f(x) = h) lim. f(x) = i) lim f(x) = x 2 3-2-
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the...
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7...
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7 sin(2x + y) + 9 cos(x - y). A. = fx(x,y) = B. = fy(x, y) = af C. ar2 = fcz(x, y) = af D. ay2 = fyy(x,y) = E. af деду fyz(x, y) = af F. მყმz = fxy(x, y) = Note: You can earn partial credit on this problem.
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x <...
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
1. The probabslity density function for x io given below. I y-x', determine the probability that...
1. The probabslity density function for x io given below. I y-x', determine the probability that y falls between 0.5 and 1.5. choose the closest answer fr (x) 0srs fx (x)-2-x 1srs2 a. 0.40 b. 0.41 c. 0.42 d. 0.43 e. 0.44 f. 0.45 g. 0.46 h. 0.47 i. 0.48 j. 0.49 k. 0.50 Answer_ 2. For the probability density function for X in problem 1, determine the 95% value of X. That is, the value of X such that...
7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.)...
7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.) fz (x,y,z) D.) Syy (x, y, z) 8.) At the Point P (1,2), find the slope of the function $(x,y) = 7x’y in the direction of ū = 43,47
Problem #7:
The graph of z = f (x, y)
is shown below. In each part, determine whether the given partial
derivatives are positive, negative, or zero. (Note that the
function is symmetric about 0 in both the x- and
y- directions.)
(a)
fx(−2, 2) and
fxx(−2, 2)
(b)
fy(−2, 2) and
fyy(−2, 2)
(c)
fx(0, −2) and
fxx(0, −2)
(d)
fy(0, −2) and
fyy(0, −2)
(A) negative, positive (B) negative, zero (C)
positive, negative (D) positive, zero (E) zero, ...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
5. Given the graph of y = f(x), shown below, answer the following, by inspection. (0.5 mark each, 4.5 marks total). 2 2 -3 -6 -7 a) f(0) = b) f(2)= c) lim f(x) = d) lim f(x) = e) lim, f(x) = d) lim f(x) = g) lim f(x) = h) lim. f(x) = i) lim f(x) = x 2 3-2-
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7 sin(2x + y) + 9 cos(x - y). A. = fx(x,y) = B. = fy(x, y) = af C. ar2 = fcz(x, y) = af D. ay2 = fyy(x,y) = E. af деду fyz(x, y) = af F. მყმz = fxy(x, y) = Note: You can earn partial credit on this problem.
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
1. The probabslity density function for x io given below. I y-x', determine the probability that y falls between 0.5 and 1.5. choose the closest answer fr (x) 0srs fx (x)-2-x 1srs2 a. 0.40 b. 0.41 c. 0.42 d. 0.43 e. 0.44 f. 0.45 g. 0.46 h. 0.47 i. 0.48 j. 0.49 k. 0.50 Answer_ 2. For the probability density function for X in problem 1, determine the 95% value of X. That is, the value of X such that...
7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.) fz (x,y,z) D.) Syy (x, y, z) 8.) At the Point P (1,2), find the slope of the function $(x,y) = 7x’y in the direction of ū = 43,47
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