Evaluate F dr where C is the line segment from (7,-,1) to (20, 1, and F (sin(yz) + 1)i + (zz cos(yz) + 2y)j + (ry cos(yz) + 2z)k. Answer:

Q: Evaluate F dr where F(r, y, z) = (2.75yz cos(ryz), 2.75rz cos(ryz), 2.75xy cos(ryz)) and C is %3D 1…

A: Here we will find out the required value.

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Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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Q: Evaluate | F· dr where F(x, y, z) (4yz cos(xyz), 4xz cos(xyz), 4xy cos(xyz)) and C is the line C 1…

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Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: Evaluate F · dr where C is the line segment from (2, -, 1) to (94, 1, and 2 2 F = (sin(yz) + 1)i +…

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Q: . Verify that u(x, y) = xy+7x +e° onjugates v(x, y) and find an expression for f(2) = f(x+iy) = u(x,…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, yo, 20) is given by the…

A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

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Q: Find the orthogonal trajectory of y = C[cos(5x – 1)]. O y? = In [sin(5x – 1)]² + C O In[- cos(5x –…

A: The given equation is, y = C[cos(5x-1)]-1

Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Find F. dr for F = 4yi + 2x j - 2z k if C is the helix x = cos t, y = sin t, z = t, for 0 <t < 4n.

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Q: If F = 2y i - zj + xk, evaluate Fx dr along the curve x = cos t, y = sin e, z = 2 cos t from t=0 to…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

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Q: Let r(t) = (sin(t), cos(t), 5 sin(t) + 4 cos(2t)). Find the projection of r(t) onto the xz-plane for…

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Q: 8. Verify that the function u(x, y) = eª sin(y) is harmonic in the region where it is defined and…

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Q: 3.) Find the directional derivate of f(x, y) = tan¹ (3xy) at the point (1,2) in the direction of…

A: We have to find  directional derivative

Q: Let z = f(x, y), x = rcos 0 and y = r sin 0. Evaluate the value of zg at the point (x, y) = (/3,1)…

A: Chain rule: If is function of and and are functions of and then, Given:

Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

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Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

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Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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Q: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

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Q: 1. (a) Let /(r,y)- cos(z + 2y). Compte the directional derivative Da/(r.y), where u- (b) Compute ff,…

A: Given that, In part (a), f(x, y) = cos(x+2y) u=(x,y)=-12,12 We have to find the directional…

Q: Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz…

A: Using the result that  ∫cF·dr=∫cPdx+Qdy+Rdz=∫P(r→(t))dxdt+Q(r→(t))dydt+R(r→(t))dzdt dt Here,…

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Evaluate F. dr where F(x, y, z) = (3.75yz cos(xyz), 3.75xz cos(ryz), 3.75xy cos(xyz)) and C is 1 1…

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Q: Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3)…

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Q: Evaluate F. dr where C is the line segment from (6,,1) to (36, 1, and F = (sin (yz) + 1)i + (zzcos…

A: Whenever a Vector is given and we need to find line integral with two points mentioned, we first…

Q: be F(x.y.=)=(6x'y- 3yz' ).i + (2x - 3xz +10 yz).j +(-6ry= + 20y:').k Find a function f such that F=…

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Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…

Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: |F - dr where C is the line segment from (6, 5,1) to (45, 1, ) and F = (sin(yz)+1)i + (zzcos(yz) +…

A: To evaluate:

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =

A: topic - partial differentiation

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: Integrate the function f (z) = (z - 8i)² from z = 0 to z = 4 + 4i along the line x = y.

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Q: Q5: Find W,e if W = f(x,y), xr cos6 and y =r sino, then prove that r Wre =-yf + xfy+ xy(fyy-fex) +…

A: The given problem is to find the double partial derivative of the given multi variable function and…

Q: 7. Let F = (2r sin(y)e", x² cos(y)e", a² sin(y)e*). %3D Find along the path c:7 = (sin(t), t,…

A: Given F→=2xsinyez,x2cosyez,x2sinyez. Find ∫CF→·dr→ along the path c:r→=sint,t,cost,-π2≤t≤π2. From…

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

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