In: Advanced Math

Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the definite integral of r(t) for 2 ≤ t ≤ 3

can you please provide a Matlab code?

Consider the vector function given below.
r(t) =
2t, 3 cos(t), 3 sin(t)
(a) Find the unit tangent and unit normal vectors T(t) and
N(t).
T(t) =
N(t) =
(b) Use this formula to find the curvature.
κ(t) =

what is the value of ∫∞−∞ δ(t+2)e^(−2t)u(t)dt?

Consider the helix
r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t).
Compute, at t=π/6
A. The unit tangent vector T=T= ( , , )
B. The unit normal vector N=N= ( , , )
C. The unit binormal vector B=B= ( , , )
D. The curvature κ=κ=

How to find the unit vectors for the following equation: r(t) =
<e^t,2e^-t,2t>
A) Compute the unit Tangent Vector, unit Normal Vector, and unit
Binomial Vector.
B) Find a formula for k, the curvature.
C) Find the normal and osculating planes at t=0

Given r(t)=ti+2sintj+2costk and u(t)=1/ti+2sintj+2costk, find
the following: 1. r(t) x u(t) 2. d/dt (r(t) x u(t) 3.now use
product rule for derivative of cross product of two vectors and
show same result

Let r(t) = 2t ,4t2 ,2t be a position function for some
object.
(a) (2 pts) Find the position of the object at t = 1. (b) (6
pts) Find the velocity of the object at t = 1.
(c) (6 pts) Find the acceleration of the object at t = 1. (d) (6
pts) Find the speed of the object at t = 1.
(e) (15 pts) Find the curvature K of the graph C determined by
r(t) when...

Find the curvature of the parametrized curve ~r(t) =< 2t 2 ,
4 + t, −t 2 >.

Find the general solution:
dx/dt + x/(1+2t) = 5

FOR THE PARAMETRIZED PATH r(t)=
e^tcos(πt)i+e^tsin(πt)j+e^tk
a) find the velocity vector, the unit
tangent vector and the arc lenght between t=0 and t=1
b) find a point where the path given by r(t)
intersects the plane x-y=0 and determine the angle of intersection
between the tangent vector to the curve and the normal vector to
the plane.

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc
length of r(t) from t = 0 to t = 5. SET UP integral but DO NOT
evaluate • What is the curvature κ(t)?

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