Exercise 2. Show that the total geodesic curvature of a simple closed planar curve is 27.

Q: For any curve in the plane, the curvature is the absolute value of the geodesic curvature. * True…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Calculate a curvature of the curve r(t) → = ⟨t,t2,t3⟩ at point (4,16,64)

A:

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: What is the curvature of the path of the motion at t=1

A: Since velocity is given we need to calculate  r''(t) only at t=1

Q: Calculate the curvature function for r

A:

Q: Find the curvature of the curve given by r(t) = 2ti + t2j −( 1/ 3) t3k.

A:

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

A:

Q: 4) Find the curvature of y = cos x at the point (÷,²). Then find the equation of the osculating…

A:

Q: what is the radius of curvature at point (1,2) of the curve 4x-y^2=0. a. 5.66 b. -5.66 c. 6.55…

A:

Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

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: Find the point on the curve at which the curvature is a maximum and (b) find the limit of the…

A: (a) To find the point on the curve at which the curvature is a maximum  (b) find the limit of the…

Q: 3. Find the curvature of f(x) = e" at point (0, 1). Then find the equation of the osculating circle…

A:

Q: Find the radius of the curvature of the curve x =y at (1, 1) +1 Hint: radius of curvature =

A: To find the radius of curvature of curve x= y3 at (1,1)

Q: Exercise 9. Show that on a simply connected surface of negative curvature two geodesics emanating…

A: We will suppose that further the Gaussian curvature of the surface is negative except for at the…

Q: Write a formula for the curvature of a plane curve with equation y = f(x). %3D

A: If the equation y=fx. Then the formula of radius curvature at the point is:   Rx=1+dydx232d2ydx2…

Q: Exercise 10. Show that the curvature of a planar curve which satisfies the equation y = f(r) is…

A: To Show- The curvature of a planar curve, which satisfies the equation y=fx is given by…

Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Exercise 5. Show that there exists at most one closed geodesic on a cylinder with negative…

A: We will assume S ⊂ R be a surface homeomorphic to a cylinder and with Gaussian curvature K < 0.…

Q: Show that curvature at an inflection point of a plane curve y = f (x) is zero.

A: We have to show that curvature at an inflection point of a plane curve y=fx is zero. We know that if…

Q: Use Theorem 11.24 to prove that the curvature of a linearfunction y = mx + b is zero for every value…

A:

Q: 138. At what point does the curve y = e* have maximum curvature?

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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

A:

Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

A:

Q: Example: Find the curvature of the curve, where a&b> o = (acos ti + asin tj + btk)

A:

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

A:

Q: Show that the curvature of a circle of radius r is K =1/ r.

A: The equation of the circle with radius r is y=±r2-x2. The upper portion of half circle equation is…

Q: At what point does the curve have maximum curvature? y = 4ex (х, у) %3D What happens to the…

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: Write a formula for the curvature of a plane curve with equation y= f(x)

A:

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

A:

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

A:

Q: Find the curvature of a superellipse defined by the parametric equations…

A:

Q: Find the radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let,  is a regular parameterization of a curve To show the curvature at  is

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: Show that the parabola y = ax2, a  0, has its largest curvature at its vertex and has no minimum…

A:

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: Exercise 3. Show that the Gaussian curvature of a surface which is home- omorphic to the torus must…

A:

Q: 10.) At what point does the curve have maximum Curvature? y=In(x). K(x)= f"|

A: firstly find f, f' and f'' . And substitute all these values in given curvature formula.  After that…

Q: Let 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and .…

A:

Q: Show that the ellipse x = a cos t, y = b sin t, a > b > 0, has its largest curvature on its…

A: Consider the given equation as x=acost, y=bsint and a>b>0

Q: 8) If curvature of a space curve at (2,3) is 8 and curvature at (7,1) t=7 is 1, what can be said…

A: Given that curvature of a space curve at 2,3 is 8 and curvature at 7,1 is 1.

Q: If 7(t) = then the curvature at the point (2,0,0) is

A:

Q: Find the curvature of rt) = Point (2,0, "2) P"(t)=(2Binf-9 Coo(3t), 0> k(4.0%)

A: Given rt=2sint, cos3t,t at point 2,0,π2r't=2cost, -3sin3t,1r''t=-2sint, -9sin3t,0

Q: Example: Find the curvature of the curve, where a&b> o r= (acos ti + asintj+ btk)

A:

Q: Find the curvature of the curve r(@) = 3Sinwî + 3Cosq ĵ + 3wCotwk %3D

A: We find the curvature with standard formula.