Question No. 1 Sketch the graph of r(t) and show the direction of increasing t. =...
(1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-< 2cos t, 5 sin t >, О r(t)- ti+ t2j + 2k t Describe the graph of r(t) 3 cos ti+5sin tj+4 cos tk (1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-,...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are length for 0 < t < 87. For the sketch, use of software is acceptable, but the graph should be drawn by hand and the right features should be present.] (b) The vector v makes an angle of with the positive -axis. Write the vector v in component form. Furthermore, write the equation of the line lt') passing through the origin with direction vector...
QUESTION 4 Given the equation of a point, r(t) ( I)i ( -I)j Sketch the graph of r(r) = (1 + l)i + (r2-Dj fr-2 2. Draw the (a) t 4 marks) position vector r(0) on the same diagram. b) Find the unit tangent vector of the point at 0 and show it on the same diagram in (a). Explain what you understand about the direction of the tangent (5 marks)
Question as above. Graph the curve C that is represented by r(t)-[t 2t also r'(0) and r() cos t], 0 2π. Graph (20 pts) 2. t (10 pts) (c) Find the length of the curve traced by r(t)-[t sint tcost t], 0StS T. (10 pts) 4. Graph the curve: r- Pl. Graph also the velocity and accerlaration vectors at t=0 and I. Give the speeds at the two times. Give the expressions for the normal and tangential components of the...
give an example of: 58. An interval a St s b corresponding to a piece of the helix r (t)costi + sint j +tk of length 10. 58. An interval a St s b corresponding to a piece of the helix r (t)costi + sint j +tk of length 10.
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...
3. Use the graph of r = f(t) and y = g(t) given below, to sketch the parametric curve: r = f(t), y=g(t). Mark with an arrow the direction in which the curve is traced when t increases. Do not try to find a formula for f(t) and g(t). Explain your work. f(0) 800 y st ont Cht 10 X 5+ -10
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...
please answer both Calculus Increasing and Decreasing Functions 1. Given the graph of f(x), sketch the graph of f'() on the same graph in a different color. PM 2. Given the graph of ''(r), sketch the graph of f(x) on the same graph in a different color. W
Sketch the requested graphs Sketch the position versus time graph whose function is r(t) = Sketch the velocity versus time graph derived from the position versus time graph Velocity versus Time u(m/s) t(s) 123 456789 10 11 12 -4