Use this theorem to find the curvature.
r(t) = 6t i + 8 sin(t) j + 8 cos(t) k
Use this theorem to find the curvature. r(t) = 6t i + 8 sin(t) j + 8 cos(t) k
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
Find the curvature of r(t) = (-7 sin(t), cos(2t), –3t) at t = ž. (Use symbolic notation and fractions where needed.) k () =
a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2<t<π/2. r(t) = (4 + t)i-(8+In(sect))j-9k, Find the tangential and normal components of the acceleration for the curve r(t)-(t2-5)i + (21-3)j +3k. a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2
2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning 2. A dragon is flying around in a pattern given by the parametric curve r(t)...
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2 2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
Find the curvature of the space curve. r(t) = -5 i + (10 + 2t)j + (t? + 8) k Ov-2021 2052 or OK 2(+1312
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
Find the curvature of the curve r(t) = (3 cos(4t), 3 sin(4t), t) at the point t = 0 Give your answer to two decimal places Preview
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR. (a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.) X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...