Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m. Marks 4 3. Find...
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
The length of the curve { et cos(t) for 0 <t<l is: y = et sin(t)
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Problem 4, Find, for 0-x-π, the arc-length of the segment of the curve R(t) = (2 cos t-cos 2t, 2 sin t-sin 2t) corresponding to 0< t < r
(1 point) Find the length of the curve (t) = (ea cos(4), et sin(), eä) for 0 st 55. Arc length =
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Please explain, thank you.
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
Question 17 Calculate the arc length of the curve r(t) = (cos: t)+ (sin t)k on the interval 0 <ts. Question 18 Find the curvature of the curve F(t) = (3t)i + (2+2)ż whent = -1. No new data to save. Last checked a
Question 11 1p Determine the length of the curve r(t) = (2, 3 sin(2t), 3 cos(2t)) on the interval ( <t<27 47107 Озубл 47 0 250 √107 None of the above or below Previous Ne
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...