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

Q: Consider points P and Q on a curve. What does it mean for the curvature at P to be less than the…

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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: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Find the curvature of the curve y = x^3 at the point (x, y) = (2, 8).

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Q: (b) Find the circle of curvature at (0, 1)of the curve y = x3 + 2x² + x +1

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Q: Find the curvature of y = sin(3x) at a = 프 4

A: We Know that The curvature measures how fast a curve is changing direction at a given point.

Q: What is the approximate radius of curvature of the function y = x2 + 6x – 96 at the point (8, 16)?

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Q: What is the approximate radius of curvature of the function y = x 2+ 6x – 96 at the point (8, 16)?

A: Given: The function is y=x2+6x-96. To determine: The approximate radius of curvature of the given…

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

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Q: What is the equation for curvature for the curvey=sin(x)? What is the curvature of the curve…

A: The equation of the circle of curvature is calculated using the formula: x-x2+y-y2=ρ2, where:…

Q: Q2 Find the radius of curvature of y5 =x at the point (x,v.). Hence, show that the radius of %3D…

A: The curve is y5=x3

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: Q2 Find the radius of curvature of yv5 = x' at the point (x, y,). Hence, show that the radius of…

A: Use formula of radius of curvature

Q: Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).

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Q: Determine the curvature of the graph of y = In x at the point where x = 1.

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Q: Find the equation of the circle of curvature of the curve y = 2x" – x at its minimum point in the…

A: The equation of a circle is defined using the formula: x-h2+y-k2=r2, where h, k is the center and r…

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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Q: Find the radius of curvature of 6y = x³ at the point (2,).

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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 the curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

Q: find the curvature at typical point (x,y) on the curve y=x²

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Q: Find the curvature of the plane curve at the pointindicated. y = t^4, t = 2

A: By Curvature we mean that to which extent any plane or graphical function is curved along onto a…

Q: Find the curvature x for the curve y = x - K = x² at the point x = 2.

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Q: Find the center of curvature of the curve y-Inx at (1, 0).

A: We Know that Centre of curvature for y=f(x) is κ=|f′′(x)|/(1+f′(x)3/2  -----(1)

Q: At what point does the curve y = e have maximum curvature? What happens to the curvature as x → ∞?

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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: Find the y coordinate of the center of curvature of th parabola at (2,2).

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Q: Consider the curve given by the equation y2+x3=0. Find its curvature at the point (−1,1).

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Q: 15. y= 2x +3 at x = 27

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Q: Find the curvature of the plane curve y=2t^4 at the point t=2 κ(2)=

A: The given curve y=2t4

Q: 1 at the point (1,1). Find the curvature of the curve f (x) =

A: We need to find the curvature of the curve fx=1x at the point 1,1.

Q: find the curvature of y=x^4 at (1,1).

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Q: Find the curvature of y = sin(-lx) at x = .

A: Solution:-

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. 32 y = 9x, x…

A: Given that Y= 9x - 32/x ; x= 4. And we find curvature and curvature of the plane at give x value.…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x3, x = 2

A: Consider the following equation of curve: y=x3 Differentiate y with respect to x: dydx=ddxx3y'=3x2…

Q: 2) Find and sketch the circle of curvature at the point on the curve y = x² where the tangent line…

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Q: Find the point on the curve y = ex where the curvature is greatest.

A: Given: Find the point on the curve y = ex where the curvature is greatest.

Q: Find the curvature of the plane curve y = 4t³ at the point t = 2.

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Q: Find the curvature of the parabola y = x² at the origin.

A: Given :-   parabola y=f(x) = x2  To find:-  curvature of parabola at origin(0,0)

Q: What is the radius of curvature at point (1, 2) of the curve 4x - y2 = 0.

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Q: Determine the radius of the curvature of the plane curve given by y In sec x at the || point (0,0).

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Q: Determine the curvature of the curve y=arctanx at x=0 and at infinity.

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Q: 2) Find and sketch the circle of curvature at the point on the curve y x where the tangent line has…

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Q: Find the radius of curvature of 6y = x3 at the point (2,). %3D

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Q: Find the curvature and radius of curvature of the curve y=cosmx at a maximum point.

A: Given curvey= cos mxWe have to find curvature and radius of curvature at maximum point .Formula…