32. The centre of symmetry of the curve y = * + 2 is at the point A. (0,0) В. (-2,0) с. (2,0) D. (0,2)

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

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

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Q: 1. Find the length of the curve y = 3 xi - () x , from x = 1 to x = 4.

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: 2 32 |for 1st<3. length of the curve c(t) =| In t,-t"

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Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: 1. Find the are length of the curve x (+ 2)/2 from y=0 to y-1

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: 3. Find the length of the curve y =x* +÷x¯² from x = 1 to x = 4

A: 3 Given function isfx=y=18x4+14x-2  from x=1 to x=4now we can writen as fx=x48+14x2 on 1,4The lenght…

Q: Find the length of the curve y=x^3/2 from the point (1,1) to the point (4,8).

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Q: 2 2 the equation of the tangent plane to the surface x² + y² + y² +2²= -1 at the point (2, -3, 4)

A: I am attaching image so that you understand each and every step.

Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

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Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

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: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

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: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

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Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

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Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

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

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Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

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Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

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: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

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Q: 6 - Find the length of the curve y = (x)7 from the x = 0 to x = 4. a) O 8/27(10^(3/2)+2) b) O…

A: .

Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

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Q: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: 1 ,3/2 y92 - y"2 between the points 3 ,1 and (6,9). 3 Find the length of the curve x=-y" 1/2

A: Given : The curve is : x=13y32-y12  We have to find the length of the given curve between the points…

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

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: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: I need to solve this question

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Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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