7) Consider the vector function r(t) = (cos(fit), In(t – 2), → a. Evaluate lim r(t)...
Find a vector function r that satisfies the following conditions. r"(t) = 7 cos 2ti + 5 sin 9tj + t?k, r(0) = i + k, r'(O) = i +j+k
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .
Using Mathematica Consider the vector-valued function r(t)=et cos t i+(sin t)/(t+4) j +t k. a) Plot the curve with t going over the interval [-2, 2]. b) Plot the curve again over the same interval, but this time add the velocity vector in blue at (1, 0, 0) to the graph. c) Plot the curve again over the same interval, along with the blue velocity vector at (1, 0, 0), but this time add the acceleration vector in red at...
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
Prob 4. Consider a complex vector space Vspan (1, cos r, sinr, cos 2x, sin 2x) with an inner product fog@dt. Let U be the subspace of odd functions in V. What is U1? Find an orthonormal basis for both U and U Prob 4. Consider a complex vector space Vspan (1, cos r, sinr, cos 2x, sin 2x) with an inner product fog@dt. Let U be the subspace of odd functions in V. What is U1? Find an orthonormal...
The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
Question 7 Let r(t) = ( 11t, cos 5t, sin 5t> Find the unit tangent vector and the unit normal vector of r(t) at + = (Round to 2 decimal places) TE == NG) = < bic rocnonse
7. Find the function f(t) that satisfies the equality f(t)dt = x-COS x + 1. 7. Find the function f(t) that satisfies the equality f(t)dt = x-COS x + 1.
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy) 3. Consider the function :R? - R. given by Flv = 0 if if (,y) (0,0): (x,y) -(0,0) (a) (1 mark] State the definition of continuity of a function at the point. (1 mark] Then calculating the limit (by any technique of your choice) show that f is continuous at (0,0). (b) [2 marks] Find the partial derivatives and at (x,y) + (0,0). and...
Evaluate f *3yxds, where pic is the vector r(t)=<sin (34), cos (-3+), Ton TH7; acte 67