The curvature of y = x2

Q: Σ=1(*) (2) Use the Integral Test to show that the series E- converges. Hint: use integration by…

A: Since you have posted multiple questions, we will solve first question for you. If you want any…

Q: Consider the given plane curve. Find the point on the curve where the curvature is maximised. What…

A:

Q: Let C(t)=((1/2)cos(t),(1/2)sin(t)) be the circle of radius 1/2 when t is from 0 to 2pi What is the…

A: Given that C(t)=12cost,12sint be the circle of radius 1/2 where t is from 0 to 2π. Here C(t) is a…

Q: Find the curvature of y = sin (1x) at x = 4.

A: we are given a one-variable function and we need to find out the curvature at the given point.For a…

Q: Write a formula for curvature in terms r1(t) and t1(t)

A: The rate of change of direction of the curve with respect to the distance along the curve is defined…

Q: Find the curvature of the curve given by r(t) = (4sin t, t, 4 cos t).

A: To find - Find the curvature of the curve given by rt = 4sint, t, 4cost     Formula used -…

Q: Calculate the curvature of the curve defined by r(t)=9cos(4t)i+9sin(4t)j. Give the answer with 4…

A: Given that: r(t)=9cos(4t)i+9sin(4t)j

Q: Use Eq. (9) to find the center of curvature to r(t) = (t 2, t 3)  at t = 1.

A: X-intercept is the point where graph of polynomial function touches/crosses x-axis, i.e y=0 . Y…

Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q1. The position vector of a moving point is given as: R()=(2 Inr) (-((+1¹) j (a) Express the unit…

A: Solution:

Q: Find the curvature k(t) of the curve (r)t=(-9sint)i+(-9sint)j+(6cost)k

A: Solution is given below:-

Q: 5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1);…

A:

Q: For r(t) = (cost, sin t, t2), find the curvature function

A: Given: rt=cost, sint, t2. To Find: The curvature function.

Q: The curvature of the curve 7 (t)= (2t, 2t+ 1, sin2t) at t= TT is 4. 1 18 O 1 1/8 1/2 O O O O

A: The given curve is r(t)→=2t,2t+1,sin(2t) We know that the curvature κ(t) for r(t)→ is given by the…

Q: Q.3 Determine all second order partial derívatives of (5) w = In(x² + y²)+ 2arctan| Mention any…

A: Given that  w=ln(x^2+y^2)+2arctan(y/x) To find the secondary order partial derivatives

Q: Given the curve f (t)= (2t2 - 3, 3 - t, 3 + 2t?). Find the equation of the line parallel to the…

A: Consider the equation as shown below: Here, curve ft =2t2-3, 3-t, 3+2t2 Here, the object is to find…

Q: Calculate the curvature of the cos(t²), sin(t²) >. Show all steps. parameterized curve r(t) =<

A: we need to calculate the curvature.