What is d²y at t = -2? dx2

Q: Find the ordinate of the center of curvature of the curve y² = 4x at point (2, 4) from the x-axis.

A: Given option are wrong, option c should be '-16'.

Q: 7. Find the radius of curvature of the curve y = In sin x at x= r/2 .

A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

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Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: Find the arclength of the curve x = 3 cos(5t), y = 3 sin(5t) with 0 <t< 20 %3D

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Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

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Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

A: Given is the integral  ∫-11 2e-3xdx The aim is evaluate the integral using trapezoidal rule.

Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: Obtain the center of gravity of the skin of the rotating object that occurs if the arc y = √9 - x2;…

A: As per the question we are given the arc : y = √(9-x2)  for  0≤x≤3 And the surface obtained by…

Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

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Q: Find the arc length of the curve with parametric equations x = e-t cost and y = e-t sint on the…

A: We have to find the arc length.

Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

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Q: Determine the length of the parametric curve given by r = 2t3, y = 3t² where 0 <t<V8. %3D CS Scanned…

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Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…

A: Given: y=18x2−ln⁡x if 18≤y≤e28−1 ⇒f(x)=18x2−ln⁡x if 1≤x≤e The arc length of the portion of the graph…

Q: Consider the parametric curve C given by X= St. y = 5 sin²t where te [0.2] (₁) Determine the values…

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Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

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 an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

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Q: 2dy -2y 2. zt at

A: Solved below

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

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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: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the gardientoff at the indicatedpoint. %3D

A: Given,

Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Find the arc length of the parametric curve: x = e'(sint + cos t), y = e'(cost - sint) OstsIn3

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).

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Q: Let C be the curve which uses straight line segments to travel from (0, 0) to (0,1) to (2,0) and…

A: The curve C is the line segments travels from 0, 0 to 0, 1 to 2, 0 and then back to 0, 0. Draw the…

Q: Find the length of the parametric curve. X =t+ sint -T<t<π | ly=t2 + cost Set up the integral, then…

A: HEre we have to find the arc length of the given parametric curve

Q: Find the equation of the tangent plane to the surface z = ly² – lz² at the point (-2, 0, -4). 4x+0

A: Given   z=y2-x2 We have to find equation of tangent line at the point(-2,0,4)

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: Find an arc length parametrization of the line y = 8x + 7. r;(s) II

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Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.

Q: Find the arc length of the curve y = t2 - 1 dt for 4 sxs6

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Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

A: I am going to solve the problem by using some simple calculus to get the required result of the…