
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find...
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
7T Find the surface of revolution if the curve (t) 3 cos(t), y(t) = 3 sin(t), for telo, is revolved around the z-axis. a) O 9V3 2 ग b) (36 - 18/3) c) O (18 - 9/3) d) Ол 7 e) 2
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
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.)
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
(3) An insect crawls along the curve (t) = (sin 21, -cos 21, 48) that has the reference point (0,1,21). (a) Find the unit tangent vector to the curve at t. (b) Find the arc length parametrization of the curve. (c) If the insect starts at the reference point(0, 1, 2n) and walks up the curve a dis- tance of 4V 2x units, what are the insect's final coordinates?
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.
Question. Consider () - ( cos(t), sin(t)) for 0 +< 2. Parameterine this curve by are length. Chat
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-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)...