Find reparametri zations two Curve aLt)=(t, Cosht, o, teR.

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 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: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point. 30 mark

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

A: The slope of the tangent is:

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: -*) at (0, 1). Find the center of curvature of the curve

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Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

Q: 4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2…

A: In a simple closed unit-speed plane curve, curvature =1r According to the question, Area of the…

Q: For a χ2-curve with 27 degrees of freedom, find the χ2-value having area 0.01 to its right.

A: It is given that, Level of significance=0.01 Degree of freedom =27 The χ2 critical value can be…

Q: at what point does the curve have maximum curvature y=7e^x

A: Given: Consider C is the curvature, formula used:

Q: Find equation of line normal to plane 3x + 2y- z = 5 and pass through Drigin point.

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Q: Find equations of the Normal plane and Osculating plane of y = 2t , the curve x = 2 sin 3t , z =…

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Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

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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: for the reparametri zations alt)= (t, Cosht, o), tER. Find two Curve %3D

A: Given curve is αt=t,cosht,0 We have to find the reparameterization for the given curve.…

Q: Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t , y = 2t, z =…

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

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: find the length of the latus rectum of the curve rsin^2x=cosx

A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

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

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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: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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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: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

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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: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

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 x for the curve y = x - K = x² at the point x = 2.

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Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

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

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Q: Chebyshev's theorem is used when there is a bell shaped curve

A: Chebyshev's theorem is used when we want to find the the upper bound  of the probability. And they…

Q: 4. z%3е-**-у", (1, 1, е-2)

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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 slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: Find equations of the Normal plane and Osculating plane of the y = 2t , curve x = 2 sin 3t , z =…

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Q: Find the length of the subtangent and sub-normal at a point of the curve X y= bsin a

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Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

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: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

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: Give arc-lengtu porametriz atian of the line which an Hhe tangent planes of and (1,2,9). is Hhe…

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

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Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given:

Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.