2. Let C be the graph of R(t) = (t sint, t³). a. Using the definition, show that Ŕ(t) is continuous at the origin. b. Find the unit tangent and unit normal vectors of R(t) to C at any real number t.

Q: Give an example of a vector-valued function 7 (t) such that its unit tangent vector T(t) is defined…

A:

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: The tangent vector to the curve is rt=3costi+3sintj+3tk , 0≤t≤π. We have to find the unit tangent…

Q: Which of the following is the directional derivative of f(z, y) = at the point (0,0) in the…

A:

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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

Q: H.W. Find the unit normal vector to the curve at t=2, r(t) = 4t i-3 t j.

A: Unit normal vector is N(t)=T'(t)‖T'(t)‖ here T(t) is unit tangent vector and T(t)=r'(t)‖r'(t)‖ So we…

Q: Let R be a vector-valued function such that R(0) = (0,2,1-2√2) and for every te R, R' (t) = (2√2…

A:

Q: Prove: If A is an m × n matrix and the column vectors of A span Rm, then A has a right inverse.…

A: Let A be an m x n matrix and the Column space of A is ℝm. To Prove: A has a right inverse.

Q: r(t) = (t cos(t), t sin(t), t)

A:

Q: Find the unit tangent vector for the parameterized curve: r(t) = 2ti + 2cos tj - 2 sint k

A:

Q: For the curve x = cos t , y = sin t , z = t, find a. an equation of the tangent line at the point…

A:

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Sketch the curve with vector equation r(t) = (t2 – 2, t) in the xy-plane. Indicate with arrows the…

A:

Q: Given r(t)=, find the unit tangent vector

A:

Q: Define a vector-valued function as follows: 7(t) = (cos t, 4, sin t). Which one of the following…

A: Find your answer below

Q: Let C be the graph of Ŕ(t) = (t sint, t³). a. Using delta definition, show that Ŕ(t) is continuous…

A: Given that R→t=t sint,t3 To find: (a) R→t is continuous at origin.              (b) unit tangent and…

Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

A:

Q: The vector function r(t)=sin 2ti−cos 2tj+t√√5k determines a curve C'in space. i. Find the unit…

A: Given: rt=sin2ti-cos2tj+t5k To find: i. The unit tangent vector T and the principal unit normal N.…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: 2. Let C be the graph of R(t) = (t sint, t³). a. Using the definition, show that Ŕ(t) is continuous…

A:

Q: 1. Let 7(t) = . a. Find the unit tangent vector at t = 4. b. Write an equation for the tangent line…

A: a. We have given r→t=t3-2t2,te4-t,2t32 Then, r'→t=3t2-4t,e4-t-te4-t,3t12 Therefore, tangent vector…