Evaluate | (x + iy' ) dz, where C is the straight line from z =1 to z=i.

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: Determine the equation of the normal line to the surface In (x + y) = Z 2 at the point (-1,2,0)

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Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: Find the equation of the tangent plane to z = In(x?y) – x/ỹ at (-,4). %3D

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: Find the normal to the curve xy + 2x – y = 0 that are parallel to the line 2x + y = 0.

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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: dy by implicit differentiatio Find

A: According to the question, we have the the equation,x7y-xy7=8we have to find dydx so,

Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: Q20:- Find the equation of the tangent plane and the normal line to the surface x2 + 4y2 + z2 - 2xy…

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Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

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Q: The orea bounded by the curve y=- ond the line xty=3 is equal to ?

A: The given curve is ,  y=2x...........(1) and the line x+y=3...........(2) we have to find area…

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…