Find the curvature and the radius of curvature at any point on the curve given by y = ln x. Simplify your answers.

Q: Find the exact length of the curve 2 y = (x²– 1)3/2, 1< x < 3. Arc length =

A: We will use the arc length formula to.find the arc length of the curve.

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: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

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

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Q: Find the tangent line to the given circle as directed. x² + y² + 10x – 6y – 2 = 0 parallel to y =…

A: Equation of the circlex2 + y2 +10x -6y -2 = 0⇒x2 + y2 + 10x -6y -2 + 25 - 25 + 9 -9 = 0           .…

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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

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Q: Find an equation for the circle of curvature of the curve r(t) = 8ti +sin(5t)j  at the point (4pi,…

A: Consider the parametrized curve y = sin ((5/8)x). its derivative can be found as follows.

Q: Find the radius of curvature of the below curve. y? = 4ax %3D

A: Solution

Q: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

Q: Find the radius of curvature of the curve r = at 0 = 1+cos 0 O 5.9665 O 5.6965 O 5.6569 5.5966

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Q: Sketch y=. Calculate the radius of curvature at x= 2 and sketch the oscillating circle.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1 や,y 3. 2 with 3 <t 5. 2. Find the arclength of the curve

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Q: gment JK and segment HK are tangents to rcle G. J

A: Given that:

Q: Use this formula to find the curvature. y = 3x4 к(x) %3 K(x)

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Q: nd the curvature of the curve ř (E)= (t-sint, I-cost,o> at the point 5I. 9. 1-cost)(-costt) =

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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 radius of curvature of the logarithmic spiral r = ae θ

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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 an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: Calculate the curvature and radius of curvature of the graph of the function y = xe

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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: Find the curvature K of the curve. r(t) = 6 cos 3nti + 6 sin 3ntj K =

A: Find the derivative r’(t) and double derivative r” (t) for the curve r (t).

Q: The arc length of the portion of the curve y =e* with 3 <x<5 is

A: Arc length formula for a curve a≤x≤b for f(x)=y is given by, L=∫ab1+dydx2 dx

Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: Find the radius of curvature of the following curve at the given point. Then write the equation of…

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Q: \B A E H BD is a A radius В tangent chord

A:

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: Use this formula to find the curvature. y = 3x4 K(x) =

A:

Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: What is the area of the largest triangle in the first quadrant with two sides on the axes and the…

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Q: Find radius and curvature at (pi/2,1) the maximum of y=sinx

A: The given function is  y = sinx To find radius of curvature at π2,1

Q: r)=(2 costia Sinst> for 6stE

A: It is given that rt=2cos3t,2sin3t differentiate w. r. t. t to get: r't=-6cos2tsint,6sin2tcost The…

Q: The curvature of y=x? is:

A: The curvature of a curve is defined as the amount by which a curve deviates from being a straight…

Q: Find the radius of curvature of the motion of r(t) = . Leave your answer correct to two decimal…

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Q: The curvature of a point moving along the curve given as R(t)=(ln sec t) i+ tj is

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Q: Find the curvature K of the curve, where s is the arc length parameter. M03 - (1+²)+(1-2) r(s) K =

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Q: Find the unit tangent vector T and the curvature k for the following parameterized curve:

A: the given curve:r(t)=9 cost , 9 sin t ,3tfirstly, differentiate the given functionr'(t)=-9sint , 9…

Q: 4) Use technology (like Desmos?) to graph each of the following functions along with its tangent…

A: Hey, since there are multiple subparts posted, we will answer first question. If you want any…

Q: Q13) the curvature of the * :circle of radius (r) is

A: Q13.The curvature of the circle of radius (r) is 1r

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: Question 10 Find the radius of curvature of y=x³ at x=1 7/ 10 A) 3 5/ 10 B 17/ 10 (C) 13 15/10 (D 13…

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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 arc length of the following line. y = 2x + 4; (0,3)

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

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

Q: Which is the complete formula used to find the radius of curvature?

A: