Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

Q: ) Find the orthogonal trajectory of the family of curve given by y = In(r³ + b)

A: First formulate a differential equation to eliminate the parameter b . Then replace (dy/dx) by…

Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

Q: Find the equation of the tangent line to the given curved as directed. x²+2y=8 perpendicular to the…

A: topic - equation of tangent line

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: Find the equation of the line tangent to Y 3x2 + x + 1 at x = -3. у 3 —17г — 26 O y = 6x – 3 O y =…

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Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x², xy), line segment from (0, 0) to (2,…

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Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A:

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Find the image of the line x = 1 under (a) flz) = z²

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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: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

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: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find the equations of the normal line to the surface z = at the point (1, - 2, 32). - t + 32 ||

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Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

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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: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is  4x+2y+z=2, that is z=2-4x-2y thus the…

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Compute the length of the curve x = 2y3 + 1/(24y) from y = 1 to y = 3.

A: Given: x=2y3+124y1≤y≤3

Q: Find the equation of the plane tangent to the grapl UI z = f(x, y) = x² + 2y³. + 1 at the points in…

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Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: Find the orthogonal trajectory to the family of curve given below y²=x²(1-Cx)

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Q: vember 12, 20Z1 m # 3 Find an equation of the tangent plane to the face at the given point. f (x,y)…

A: Solve the given problem.

Q: Show that the curve In (2X-1) , n> i has no stationary point

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Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: An automobile, traveling at a constant rate, starts at home at ime t = 0 and ends up 10 hours later…

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Q: Find the length of the curve defined by R(t) = (3t+1, 4t³/2, 4 - 3t²) from the point (1,0, 4) to (4,…

A: Given…

Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

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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: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

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Q: O whion of the line: y--2x+8 Poliowing line5 ave perpendicular to this. B. ut

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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 equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.