Homework Answers
Answer is B
Because we know that the maximum rate of change of function is given in direction of grad f(x,y)
clearly to find unit vector we just need to divide grad(f(x,y)) by its magnitude.
option B is exactly doing that,hence is correct option
Add Answer to:
(8) 2 points Let f be a function defined and continuous, with continuous first partial derivative at the origin (0,...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) i...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
(1 point) Let f(2) be a function that is defined and has a continuous derivative on...
(1 point) Let f(2) be a function that is defined and has a continuous derivative on the interval (2,). Assume also that f(2)= -9 f(x) <z +5 and $,* f(z)e 2/5 dr ==8 Determine the value of $,° 6'(a)e 7/5 dz
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
(1 point) Let f(a) be a function that is defined and has a continuous derivative on...
(1 point) Let f(a) be a function that is defined and has a continuous derivative on the interval (2,00). Assume also that f(3) = 6 \f (2) < 208 + 2 and f(xv)e 3/6 da = 5 Determine the value of $'(x)e-7/5 da
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x,...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E...
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E (0, 1). Suppose Vr,y(0,1) IF f'(x) 0 and f'(y) ±0 THEN f'(x) af'(y) Show that there is exactly f(ax) and f'(x) 0 such that f(x) one Hint: Suppose f(x) is a continuous function on [0, 1] and f(0) x € (0, 1) such that f(x) = f(ax) f(1). Let a e (0,1), there exists an
Suppose f is a continuous and differentiable function on...
The partial derivative Let ei denote the ith standard basis vector of R The ith partial derivativ...
The partial derivative Let ei denote the ith standard basis vector of R The ith partial derivative of f : R" - R is defined by Select one: h-0 b. I inn f(x+he,)-f(x) O Th O c lim h-0 d. none of the other options O f(x+he,)-f(x) h-0 O e lim
The partial derivative Let ei denote the ith standard basis vector of R The ith partial derivative of f : R" - R is defined by Select one: h-0...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
(1 point) Let f(2) be a function that is defined and has a continuous derivative on the interval (2,). Assume also that f(2)= -9 f(x) <z +5 and $,* f(z)e 2/5 dr ==8 Determine the value of $,° 6'(a)e 7/5 dz
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
(1 point) Let f(a) be a function that is defined and has a continuous derivative on the interval (2,00). Assume also that f(3) = 6 \f (2) < 208 + 2 and f(xv)e 3/6 da = 5 Determine the value of $'(x)e-7/5 da
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E (0, 1). Suppose Vr,y(0,1) IF f'(x) 0 and f'(y) ±0 THEN f'(x) af'(y) Show that there is exactly f(ax) and f'(x) 0 such that f(x) one Hint: Suppose f(x) is a continuous function on [0, 1] and f(0) x € (0, 1) such that f(x) = f(ax) f(1). Let a e (0,1), there exists an
Suppose f is a continuous and differentiable function on...
The partial derivative Let ei denote the ith standard basis vector of R The ith partial derivative of f : R" - R is defined by Select one: h-0 b. I inn f(x+he,)-f(x) O Th O c lim h-0 d. none of the other options O f(x+he,)-f(x) h-0 O e lim
The partial derivative Let ei denote the ith standard basis vector of R The ith partial derivative of f : R" - R is defined by Select one: h-0...
Most questions answered within 3 hours.
-
Katelynn, a physician, earns $200,000 from her medical practice
in the current year. She receives $45,000...
asked 5 minutes ago -
Each row of the table below describes an aqueous solution at
25°C
.
The second column...
asked 10 minutes ago -
A horizontal wire is at y = 0. Current travels in the +x
direction. The magnetic...
asked 10 minutes ago -
Let X be a continuous random variable whose PDF is Let X be a
continuous random...
asked 31 minutes ago -
Martinez Company’s relevant range of production is 7,500 units
to 12,500 units. When it produces and...
asked 29 minutes ago -
A football with a mass of 1.2 kg is kicked from ground level to
a height...
asked 35 minutes ago -
Remember: Changes in supply determinants shift supply, and
changes in demand determinants shift demand. We say...
asked 34 minutes ago -
Why is the answer b), for this question? I came up with C) for
my incorrect...
asked 40 minutes ago -
Suppose that you know that in the population of full-time
employees in the United States, the...
asked 1 hour ago -
This experiment was designed originally to sample various meat and carcass quality
aspects of Ontario pigs...
asked 1 hour ago -
Dopamine Hydrochloride: draw the structure And Show the
functional groups in different colors and label the...
asked 54 minutes ago -
A rope supports a 10 kg dumbbell hanging from it. What is the
tension in the...
asked 54 minutes ago