If u(t) = sin(2t), cos(2t), t and v(t) = t, cos(2t), sin(2t) , use Formula 5 of this theorem to find d dt u(t) × v(t) .
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
all parts
-2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
The trajectories of two particles moving in R3 are described by 10) = (a sin(e, sin(), 5 coses) and r2(t) = (sin(2t), 2 sin?(t), 2 cos(t)) for tER. a) Show that one of these trajectories lies on a sphere S centered at the origin in R3, and that the other one is contained in a plane. In what follows, we denote by r(t) the position of the particle that lies in a sphere. b) Prove that r(t) is orthogonal to...
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
1. Sketch the graph of x(t) = sin(2t),y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph
1. Sketch the graph of x(t) = sin(2t),y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and...
Question 9 Let r(t)={cos 2t, sin 2t, V5t) a) Find the unit tangent vector and the unit normal vector of r(t) at += TI (Round to 2 decimal places) TE)= NG) = < b) Find the binormal vector of r(t) at t = TT 2 (Round to 2 decimal places) BC) =< A Moving to another question will save this response.
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...
(1 point) a. Find the Laplace transform F(s)-f(t)) of the function f(t)-7+sin(2t), defined on the interval t 0 F(s) = L(7 + sin(2t)) = help (formulas) b. For what values of s does the Laplace transform exist? help (inequalities)