1. Find t(s), n(s), b(s), k(s), T(s) for the following curves (don't forget to reparametrize by...
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
Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 2t i + (2 − 3t) j + (8 + 4t) k r(t(s)) =
Plane Curves Find T, N, and K for the plane curves in Exercises 1-4 1,/r(t) ti (In cos j, /2 <t< T/2
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Hi need help for these Questions: a. Given f = yi + xzk and g = xyz2, determine (∇ x f ) . ∇g at the point (1,0,3) b. Point A lies on the curve r(t) = 2 cos t i + 2 sin t j + t k for the range 0 ≤ t ≤ 2π . At point A, the tangent vector is T = - 21/2i + 21/2j + k. Determine the co-ordinates of point A and...
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t). (1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t) (1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t)
Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (3t+2, 5t - 7,67 +12) T= 000 (Type exact answers, using radicals as needed.) JUNIL Score: 0 of 2 pts 42 of 60 (58 complete) HW Score: 72.17%, 7 X 14.4.40 Ques Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. r(t) = (7+2,8%. 31), for 1sts Select the...
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. 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.