- A vector tangent to the parametric curve given by r (t) =
<cos (4t); sin (4t); e^(t^2)> at the point
(0; 1; e^((pi/8)^2)) is
a) (0; 1; e^((pi/8)^2))
b) (0; 4; e^((pi/8)^2))
c) (4; 0; e^((pi/8)^2))
d) (4; 4; e^((pi/8)^2))
e) None of the above
- The curve c (t) = (cost, sint ,t) lies on which of the
following surfaces:
(a) cone
(b) cylinder
(c) sphere
(d) plane
(e) none of the above
- A vector tangent to the parametric curve given by r (t) = <cos (4t); sin...
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal (a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that all of your answers should be numbers (1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K...
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0). uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...
a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2<t<π/2. r(t) = (4 + t)i-(8+In(sect))j-9k, Find the tangential and normal components of the acceleration for the curve r(t)-(t2-5)i + (21-3)j +3k. a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the plot of the curve? IV 20 50 (a) Compute the arc length of the curve from t = 0 to t = 3. (b) Find the unit tangent vector T(t). (c) Compute the curvature of the curve at any value of t. 12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the...
I have no idea how to go about this question. Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and a plane. Find the curvature at an arbitrary point on the curve. Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and...
Find the slope of the tangent line to the Lissajous curve cos(t), y = sin(4t) at t = 1/6. Eliminate the parameter to find the Cartesian equation of the curve x = 41-t, y = (1+t, -1st s 1. Identify what type of curve this is. You do not have to sketch the curve.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.