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2. Copy the given set onto your homework, and then express it either by listing the...
2. Compute | F. ds for each of the vector fields F and paths r given...
2. Compute | F. ds for each of the vector fields F and paths r given below: (b) Ple:) - (a ) and re) – () witte (0.1 Fler,1,2) = ( and r(t) = ( ) with t e (0, 2). F(x, y, z) = | 22 and r(t) = with t€ (0,2). F(x, y, z) = sin Cos y 32 and r(t) = -t with t € (0,1). (a) F(x, y, z) = | Vies:)-( .) --( * )-464...
correct answers 135. Computer Graphics. One of the most important applications of linear transformations is...
correct answers
135. Computer Graphics. One of the most important applications of linear transformations is computer graphics where we wish to view 3-dimensional objects (for example a crystal) on a 2-dimensional screen. The screen is the ry-plane. The aim is to rotate the crystal and orthogonally project it onto the ry-plane to obtain different views of it. We consider 3 possible rotations: 0 . A rotation of θ round the x-axis using the matrix R2-10 cos θ -sin θ cos...
Set theory Find f(A) and f-(B) for the given function and sets. (a) f : R...
Set theory
Find f(A) and f-(B) for the given function and sets. (a) f : R → R is defined by f(x) = x2 + 1, A = [-1,2], B = [0,4]. (b) f R R is defined by f(x) - sin z, A [0, ], B [0,2]. (c) f : R → Z is defined by f(x)-번 (the floor function), A = (0,4], B-(0,1,2). (d) f : R-(0) → R is defined by f(z) = x + 1, As...
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivativ...
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivative of u at (x, t) = (zo, to) along v is Dvu(x, t) = ▽u(ro, to) , v b) Solve the following homogeneous linear transport equation ul + uz = 0, u(x,0) =-2 cosx c) Solve the following non-homogeneous equation ut-2uz--2 cos (x-t), u(x, 0) = sin x d) Solve the following second-order homogeneous linear euqation u(z,0) = sin x, ut (z,...
Express the unit vectors, , φ in terms of 8,9, 2 (that is, derive Eq. 1.64)....
Express the unit vectors, , φ in terms of 8,9, 2 (that is, derive Eq. 1.64). Check your answers several ways ( f . f = 1,0 . φ 0, f × ยิ p, you need to check all of these explicitly, the solution manual does not give all of these). Also work out the inverse formulas, giving £,9,2 in terms of f, θ and θ, φ). sn θ cos φ x + sin θ sin φ y + cos...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Question 1. Determine whether or not
Question 1. Determine whether or not \(\mathrm{F}(x, y)=e^{x} \sin y \mathbf{i}+e^{x} \cos y_{\mathbf{j}}\) is a conservative field. If it is, find its potential function \(f\).Question 2. Find the curl and the divergence of the vector field \(\mathbf{F}=\sin y z \mathbf{i}+\sin z x \mathbf{j}+\sin x y \mathbf{k}\)Question 3. Find the flux of the vector field \(\mathbf{F}=z \mathbf{i}+y \mathbf{j}+x \mathbf{k}\) across the surface \(r(u, v)=\langle u \cos v, u \sin v, v\rangle, 0 \leq u \leq 1,0 \leq v \leq \pi\) with...
need help with these.please. I-8 Let f(2) Find the open intervals on which fis increasing (decreasing)....
need help with these.please.
I-8 Let f(2) Find the open intervals on which fis increasing (decreasing). Then determine the x-coordinates of +8 all relative maxima (minima). 1. f is increasing on the intervals 2. fis decreasing on the intervals 3. The relative maxima of f occur at - 4. The relative minima off occur at 2 - Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such...
QUESTION 9 Set up the iterated integral for evaluating S SS Fr, 0, 2) dz r...
QUESTION 9 Set up the iterated integral for evaluating S SS Fr, 0, 2) dz r dr de over the given region D. D D is the right circular cylinder whose base is the circle 1-2cose in the xy-plane and whose top lies in the plane 26-x-y. cos sin ) S" s2.com fit, 0, 2) dar dr de 0 sin e 6-sin-coso 52" s 'S ft , z) dar dr de so 0 0 0 0 2 cos 0 -pleos...
Please solve these 3 questions and please give me a detailed explanation for your answer. Hopeful...
Please solve these 3 questions and please give me a detailed
explanation for your answer. Hopefully your answers are correct.
Please help me out because I am stuck on how to solve these
problems for a long time.
4. Which is the solution for a(0, y) = 0, u(1,y) = 0 u(z,0)=2sin(3xx), lim u(z,y)=0? B. 2e-3ry sin(3nx) C. 2sinh(3Ty)sin(3T) D. 2sinh(3Ty) cos(3Tx) E. none of the above 5. If y" + 3y' +2y = δ(t _ 2) with y(0) =...
2. Compute | F. ds for each of the vector fields F and paths r given below: (b) Ple:) - (a ) and re) – () witte (0.1 Fler,1,2) = ( and r(t) = ( ) with t e (0, 2). F(x, y, z) = | 22 and r(t) = with t€ (0,2). F(x, y, z) = sin Cos y 32 and r(t) = -t with t € (0,1). (a) F(x, y, z) = | Vies:)-( .) --( * )-464...
correct answers
135. Computer Graphics. One of the most important applications of linear transformations is computer graphics where we wish to view 3-dimensional objects (for example a crystal) on a 2-dimensional screen. The screen is the ry-plane. The aim is to rotate the crystal and orthogonally project it onto the ry-plane to obtain different views of it. We consider 3 possible rotations: 0 . A rotation of θ round the x-axis using the matrix R2-10 cos θ -sin θ cos...
Set theory
Find f(A) and f-(B) for the given function and sets. (a) f : R → R is defined by f(x) = x2 + 1, A = [-1,2], B = [0,4]. (b) f R R is defined by f(x) - sin z, A [0, ], B [0,2]. (c) f : R → Z is defined by f(x)-번 (the floor function), A = (0,4], B-(0,1,2). (d) f : R-(0) → R is defined by f(z) = x + 1, As...
2. Let u(z,t) be a differentiable function on R x [0, 0o). a) Show that the directional derivative of u at (x, t) = (zo, to) along v is Dvu(x, t) = ▽u(ro, to) , v b) Solve the following homogeneous linear transport equation ul + uz = 0, u(x,0) =-2 cosx c) Solve the following non-homogeneous equation ut-2uz--2 cos (x-t), u(x, 0) = sin x d) Solve the following second-order homogeneous linear euqation u(z,0) = sin x, ut (z,...
Express the unit vectors, , φ in terms of 8,9, 2 (that is, derive Eq. 1.64). Check your answers several ways ( f . f = 1,0 . φ 0, f × ยิ p, you need to check all of these explicitly, the solution manual does not give all of these). Also work out the inverse formulas, giving £,9,2 in terms of f, θ and θ, φ). sn θ cos φ x + sin θ sin φ y + cos...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
need help with these.please.
I-8 Let f(2) Find the open intervals on which fis increasing (decreasing). Then determine the x-coordinates of +8 all relative maxima (minima). 1. f is increasing on the intervals 2. fis decreasing on the intervals 3. The relative maxima of f occur at - 4. The relative minima off occur at 2 - Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such...
QUESTION 9 Set up the iterated integral for evaluating S SS Fr, 0, 2) dz r dr de over the given region D. D D is the right circular cylinder whose base is the circle 1-2cose in the xy-plane and whose top lies in the plane 26-x-y. cos sin ) S" s2.com fit, 0, 2) dar dr de 0 sin e 6-sin-coso 52" s 'S ft , z) dar dr de so 0 0 0 0 2 cos 0 -pleos...
Please solve these 3 questions and please give me a detailed
explanation for your answer. Hopefully your answers are correct.
Please help me out because I am stuck on how to solve these
problems for a long time.
4. Which is the solution for a(0, y) = 0, u(1,y) = 0 u(z,0)=2sin(3xx), lim u(z,y)=0? B. 2e-3ry sin(3nx) C. 2sinh(3Ty)sin(3T) D. 2sinh(3Ty) cos(3Tx) E. none of the above 5. If y" + 3y' +2y = δ(t _ 2) with y(0) =...
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