© Find the Unit. Tangent Vector of the the eurire r 4) =(3+) -(4+1); Fotki 1...
Find the unit tangent vector for the given vector function. r(t)=< 3+t2 ,t4, 6>
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)-- EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
Question 7 Let r(t) = ( 11t, cos 5t, sin 5t> Find the unit tangent vector and the unit normal vector of r(t) at + = (Round to 2 decimal places) TE == NG) = < bic rocnonse
12.3.6 Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = 6t’i + 2tºj - 31ºk 1sts2 The curve's unit tangent vector is (i+(Oj+(k. (Type an integer or a simplified fraction.)
12.3.3 Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = 2ti + () 'k, Osts5 The curve's unit tangent vector is (i + (O; + (Ok. (Type exact answers, using radicals as needed.)
(1 point) Given R' (t) R' (t)ll Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t)- N(t) (1 point) Given R' (t) R' (t)ll Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t)- N(t)
12.3.8 Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (5t sint+5 cos t)i + (5t cost-5 sint)j V2 sts2 The curve's unit tangent vector is (i+j+ K.
(1 point) Find a vector equation for the tangent line to the curve r(t) = (2/) 7+ (31-8)+ (21) k at t = 9. !!! with -o0 <1 < 0
(b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
3. [-/10 Points] DETAILS SCALCET8 13.2.017. Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = - 3t, 1 + 4t, = { + t = 4 T(4) =