The formula k(x) = expresses the curvature of a twice-differentiable plane curve as a function of x. Use this formula to find the curvature [1+ (r'(x)?]/2 function of the following curve. f(x) = - 9x2 The curvature function is K(x) = |

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

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Q: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

Q: For the function graphed below, estimate the point of greatest curvature -4 -3 -2 -2 -3

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Q: At what point does the curve have maximum curvature? What happens to the curvature as x→∞ 30. y=1n x…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: alculate the curvature and radius of curvature of the graph of the function y=√x at x=1.

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Q: Find the radius of curvature at any point on parabola y2=4ax

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Q: Which of the following points do not lie on any tangent line of the parabola y=x2+2

A: given parabola is                                                           y=x2+2 any point on the…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: determine the maximum curvature for thegraph of each function.27. ƒ(x) = ln x

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Q: Find the equation of the tangent plane to the graph of g(x, y) = ln(6x² – 3y²) at the point (1, 1).…

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Q: Fnd all points on the graph of the function such that the curvature is zero.      y = (x − 2)6 + 3x

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Q: Does the graph of Sx²sin (1/x), x ± 0 f(x) = lo, x = 0 have a tangent line at the origin? Give…

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: For the function graphed below, estimate the point of greatest curvature. 43 Submit Question

A: We have to find greatest curvature of the function in graph

Q: Determine the maximum curvature for the graph of ​f(x)=5ln(8x).

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Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Find and sketch the circle of curvature at the point on the curve y = x2 where the tangent line has…

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Q: Find the length of the curve y = 1 - e^-x, 0 <=x<=1.

A: The given curve is

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: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan , (7,0, 0)

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Q: The curvature of y =x is

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: The equation of a curved road is given as y = 100+6x–0.015x² +0.0000111? Determine the places where…

A: The equation of the curved road given is: y=100+6x-0.015x2+0.00001111x3 Measure of the "Sharpness of…

Q: Find the curvature K of the curve C x² 1 16 9. at the point (0, 3)

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Q: 2. Given the function y =+*- r*+x* - 3x + 21 (-1.5 < x < 1), find the slope and curvature for the…

A: Given the function

Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: 3) Let x = t2 - 1 , and y = e2 . Find the tangent line to the point (0, 1) .

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Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

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Q: Find the equation of the tangent plane to the graph of f(x, y) =−3x2 − y3 at the point (x, y) = (2,…

A: The given function is

Q: Determine the maximum curvature for the graph of f(x) = 9 In (8x). The maximum curvature is at x=

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Find the curvature k of the curve C: 16 + =1 at the point (0, 3)

A: To find the curvature of the curve at the point (0,3).

Q: The path of a particle's motion is defined by y = x2 + 3x, where the dimensions are measured in cm.…

A: The radius of curvature of the curve y=f(x) is expressed as ROC=1+dydx232d2ydx2 Differentiate both…

Q: For the function graphed below, estimate the point of greatest curvature -4 -3 /-2 -1 -2 (0,-2) x…

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Q: For the function graphed below, estimate the point of greatest curvature 1.

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Q: Find the point on the curve y = (x − 8)² +9 at which the curvature K is a maximum.

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Q: Find the radius of curvature at any point x = - of the curve

A: Given,             y=4sin2x-sin4x at  x=π4

Q: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

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Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).

A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0…

Q: Find an equation for the tangent line to the parabola y x*at the point P(1, 1). %3D

A: Given,            The parabola is y=x2 and the point is P1,1.We know that,            The equation…

Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: Find the equation of the tangent plane to the graph of xe*y- eyz = In(x?) at the point (1,1).

A: Solution

Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )