3,2 Given f(x, y) = sin(x + y) where x = s°t, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = f:(æ(s, t), y(s, t)) = Note: This question is looking for the answer to be only in terms of s and t

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: Given f(x, y) = = s°t?, y = 3s – 2t. Find sin(z + y) where z f.(z(s, t), y(s, t)) = cos( st2 + 35-…

A: Given f(x,y)=sin(x+y)where x=s3t2,y=3s-2t

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Q: Given f(x, y) = sin(x + y) where x = s*t°, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = f:(æ(s, t), y(s,…

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Q: 3x Given f (x,y) =4e* In y with x = In (u cos t) and y = u sin t. The correct value of dz evaluated…

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Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: Given f(x, y) = sin(x + y) where a s*t°, y = 2s – 6t. Find f.(x(s, t), y(s, t)) = fi(#(s, t), y(s,…

A: we have calculate the f_s( x(s,t) ,y(s,t)  and f_s( x(s,t) ,y(s,t)

Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: (a) if f (t) = te“ cos 5t then L{f (t)} =?. %3D 4s2 + 19s + 52 (b) if F (s) then L-1{F(s)}=? %3D s…

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Q: dw Q/Answer the following - ar ,w = (x + 3y + z)², x = r3 – s², y = tan(r + s) ,Fsin(r+s) at the…

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Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: If 1 = T T (xyz – 3xy)a, + (zy² + 3x² )a, + xy a,] V(x? + y?) And B = r² a, + sin 0 aø Find |A x B|…

A: Given: B→=r2ar+sinθaϕ It is known that r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx. At P1, 2, 4, obtain…

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x*yt cos(2)) 4,4 fm = fu f2 =

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (b) z = x2 + 3xy + y2 ; x = sin s + cos t, y = sin s - cos t

A: Consider z=fx,y & x=fs,t, y=fs,t Then, the derivative of z with respect to s is given by:…

Q: dw when r= 3 and s = - ar 3 if w = (x+ y + z)“, x=r-s, y= cos (r + s), z= sin (r + s). Find

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Q: The functions y,(t) = sin(2t), y,(t)= cos(2t) are linearly independent on (-0, x). Select one: OTrue…

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Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: Solve the following problems. Зху 1. Given that f(x,y, z) = e*' cos(yz). Find f , fw frvi: xyz ху

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: Evaluate [P r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ F. dr where F = (4z, - 3y, 2x), and C is given by

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Q: Given f(x, y) = sin(x + y) where x = s°t2, y = 6s – 2t. Find f.(x(s, t), y(s, t)) = fe(x(s, t), y(s,…

A: From starting itself if we replaced x and y interms of s and t in f we can easily work in that.

Q: dw and ar aw Q2) Find if əs w = 2x – y? + z°, X = sin (s), y=tan (r - s), z=r e°. %3|

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Q: 3. Find an equation of the form y = ab* + c sin (“x) that fits the data below x | 0 1 | 2 |y | 4 |…

A: To find the equation of the form y=abx+csin(π2x) which fits the data  x0123y4111629

Q: Evaluate [P F = (4%, F(t)= (t, sin(t), cos(t)), 0≤ t ≤ T F. dr where 3y, 2x), and C is given by

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Q: N 1 1 202 2{(xn – µ)²}– z(Ord – r). n=1

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

Q: (d) i– 2i +x = te given that at t=0, x = 1 and i = 0.

A: The solution of given differential equation is given as follows :

Q: Find D (x, y, z) where f(x, y, z) = cos(z²)sin(y²) In the direction of v = (4, 15, 18). %3D Possible…

A: Introduction: The formula for the directional derivative of the function f(x,y,z) in the direction…

Q: Given f(x, y) = sin(x + y) where x = s°t, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = ft(x(s, t), y(s,…

A: Given that: f(x,y)=sin(x+y)x=s3t2y=3s-2t

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: S(z, y, 2) = 122 y sin(z) – Vy- z cos(r+y) 8PR Find Vf.

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Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: Given f(x, y) = sin(x + y) where x = s°t4, y = 6s – 4t. Find f.(x(s, t), y(s, t)) = f:(#(s, t), y(s,…

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Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find fy(5,5,0). Leave your answer correct to two decimal %3D…

A: Partial derivatives

Q: 37. F(x, y, z) = xi + yj + zk C: r(t) = 2 cos ti + 2 sin tj + tk, 0 < t < 2n

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Q: R. 4, = U, - sin x cos t, :>r > 0 B.C.: «(0, t) = 0, 1.C.: u(x, 0} = 0, 1,(x. 0) = 0

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Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

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Q: Given f(x, y) = sin(x + y) where x = = s*t*, y = 3s – 4t. Find - f.(x(s, t), y(s, t)) = fi(x(s, t),…

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Q: Find ∂w∂s and ∂w∂t when s = 1 and t = 2π for w = xy + yz + xz                    where x = s cos…

A: Given: w=xy+yz+xz where x=scos(t), y=ssin(t), z=t at s=1 and t=2π

Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: Given f(x, y) sin(x + y) where x = s*t, y = 4s – 2t. Find f.(x(s, t), y(s, t)) = fi(r(s, t), y(s,…

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Q: 2. Which of the following can be differentiated easily without using the Chain Rule? х (b) y = + 2)…

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Q: 2,5 Given f(z, y) sin(x + y) where 2s 5t. Find f.(ar(s, t), y(s, t)) f(x(s, t), y(s, t)) =| Note:…

A: It is given that f (x, y) = sin (x + y) where x = s2t5 and y = 2s–5t.

Q: Find D (z,y, z) where f(r, y, z) = r" cos(y")cos(z) In the direction of v = (-9,16, 13). Possible…

A: Directional Derivative of a Scalar Point Function Definition: Let fx, y, z be a scalar field in a…

Q: Q/Answer the following dw W = ar = (x + 3y+ z)², x = r³ – s², y = tan(r + s) Fsin(r+s) at the point…

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Q: By about how much will h(x, y, z) = cos (paixy) + xz2 change if the point P(x, y, z) moves from…

A: The given function is,

Q: We have r(t) = (2e-t, sin-'t, In(1 –t)) , %3D Find 1- The domain 2- ar , an, T, N and t at t=1

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