Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and below Jby the liney=

Q: *Gl0/ Apply Stoke's theorem to Cal cu late S4y dx +2zdy + 6y dz where c i$ the curve of xyt 2 = 6z…

A: Apply Stokes theorem to calculate ∫C(4ydx+2xdy+6ydz) where c: intersection of x2+y2+z2=6z and z=x+3…

Q: Let F(x,y,z) = (z2,x,y}, and let C be the curve that is given by r(t) = (3 + 5t2,3 - t2,t} for 0 ≤ t…

A: Given: F(x,y,z)=z2,x,y and rt=3+5t2, 3-t2, t for 0≤t≤2

Q: (3) Compute f ds over the curve specified. (a) f(x, y, z) = 2²,r(t) = for 0 for 0 < t < 1

A: Consider the equation

Q: 15. Find the equatio.f.the. tangent.plane..bo. the given.sur.face.at.thespei fied. praint. 2…

A: solution is given below..

Q: Let r(t) = E (3t — 3, 5е", — 5е"). Find the line (L) tangent tor(t) at t = - 1. - L: (x, y, z) +t

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Q: B) Evaluate the line integral F-dr, where F (x, y) = r*y°i+x²y°j and C is the curve r (t) = (t³ +…

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Q: F(x,y) = (1+2xy²)î+(2x²y +2y)j (i) Show that F is conservative and find f such that Vf = F. (ii)…

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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. x'dz +z?dy +y?dx where C is the curve x = t ,y = t2, z = t? from t = 0 to t = 2.

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Q: Let F = (2y2, 4x²), and let C be the curve y = x-1 for 1 s x < 4, oriented from left to right.…

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Use Green's Theorem to find the work done by F(x,y)=x(3x+y)i+xy^2j in moving a particle from the…

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk

A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk   To determine: The values of the unit…

Q: Find the work done by F = - 2zi + 7xj + 5yk over the curve C in the direction of increasing t. C:…

A: Solution of this question is

Q: Let f (2) = zi + (z – 4). || Part (a) Integrate the function f (z) along the curve C given by z =…

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: 17) Find the area of te senface genereted by revolving the curve X=3¢, y= 2f about fue x-qxis on tue…

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Q: Consider z as a function of æ and y and z = Ax + By + D be the tangent plane to f(x, y) = 2a² + 2y³…

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Q: Q4. Let C be a portion of a curve from (2,0) to (2, 2). Let F(r, y) = (tan(2²) + e²", 2.re²y + cos…

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Q: Find the work done by F = 2xy°i + 9x<y*j in moving a particle once counterclockwise around the curve…

A: The solution is given below:

Q: F(x, y) = (4xy³ + 3)i + (6x²y² + 2e?" is conservative by finding a potential function f for Fl and…

A:

Q: Let F = e'i+(xe' -e')j- ye'k and cbe a smooth curve defined by Then the value of the line integral…

A: The formula is  ∫F.dr=∫F(r(t)).r'(t)dt Here…

Q: 3.) caiculate S FC().dr, wmere = a:l F=X"ityj;c:Y=1-x?:fromx =1Untix=1 b) Petemine the woru done by…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 3xyi + 4yj - 2yzk r(t)…

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Q: Consider the one-form w = dx +g' (y) dy on R², where g : R →Ris an arbitrary smooth function. Show…

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Q: Calculate fc (zy + + z) ds along the curve F(t) = 2ti +tj + (8 – 2t)k where 0 <t<1 %3D a) 26 b) 23…

A: Given - The curve r→t = 2ti^ + tj^ + 8 - 2tk^ where 0 ≤ t ≤ 1 To find - Calculate ∫Cxy + x + zds…

Q: Let G(x. y)=x*yi+(y+xy*)j. Evaluate the line integral [G-dr, where Cis the curve x= ť and y=t* for…

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Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

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Q: Consider Fand C below. F(x, y, z) = yzex2i + exj+ xyeXk, C: r(t) = (t2 + 4)i + (t2 – 2)j + (t2 -…

A: Solve using fundamental theorem.

Q: Find the work done by F over the curve in the direction of increasing t. F= 11zi + 11xj + 11yk, r(t)…

A: We have to find the work done by F over the curve

Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, æ + 3z, 2x + 3y) (b) If C' is the curve…

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Q: 13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized…

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Q: Find an equation of the tangent plane to the surface z = In(2x + y) at the point P(-1,3, 0) Select…

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Q: find the work done by F over the curve in the direction of increasing t. F = 2y i + 3x j + (x + y)k…

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Q: For F(x, y,z)=(6xsin y+10xz' )i+(3x cos y-4ye"-2y ze" ) j+(-2y'e* +15x²z² )k , find | a function f…

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Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

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Q: 3. Evaluate the line integral c F. dr where F(x, y, z) = (e², xz, (x + y)) with 0 ≤ t ≤1 over the…

A: The solution is given as

Q: find the work done by F over the curve in the direction of increasing t F = 6z i + y2 j + 12x k r(t)…

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Q: 3. If Ø = 2xyz?,F = xyî – zĵ + x²k and C is the %3D curve x = t2, y = 2t, z = t³from t = 0 to t = %D…

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Q: Let f(2) = zi+ (z – 7) Part (a) Integrate the function f(2)along the curve C given by z= B +iftrom…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: F=2xi + 2y=j+y** the line integral [F.dr overthe curve c live r(t) =ri+tj+e'k, 0 sislis equal to

A: The vector field given is a line integral.

Q: Civen tz f(x,y) = J 36-9x=y

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: F(x, y) = xi + yj C: r(t) = (9t + 2)i + tj,      0 ≤ t ≤ 1

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Q: The value of [F.dr where F= x'y2 i + y j and C is the curve y? = 4x in the XY-plane from (0, 0) to…

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Q: Find the work done by F over the curve C in the direction of increasing t,where F=-5 yi+5xj+8z°k and…

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Q: F(r, y) = (2xy³ +3)i+ (3x²y² + 2e²»)j is conservative by finding a potential function f for F, and…

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Q: Show F(x, y) = (2æy³ + 8)i + (3x²y² + 2e2")j is conservative by finding a potential function f for…

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Q: Let F(x. y. z) = (3x y: - 3y) i (x'z - 3x) j + (x'y+ 2:) k Evaluate , F dr. where C is the curve…

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Q: (1) Let f(x, y) = xe" + x2. (a) Find the tangent plane of f at the point (2,0). (b) Use your answer…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.