1. Consider the vector-valued function F(t) = sin(2t) t (2, 1, -2), a) Find the domain of F. b) Show that is continuous at t = 0. t ' 1 - V₁ +1) " +t , et, t #0 t = 0.

Q: Find the domain of r(t) and the interval(s) on which the vector- valued function is continuous. r…

A: We need to find the domain and the interval on which the vector-valued function is continuous.

Q: Define two vector functions 7(t) = 2 sin(t)i + 8 cos(t)j + t°k ü(t) = 8 sin(t)? + 2 cos(t)j + (t? –…

A:

Q: Let 7 (t) = (t + 5, 5e“, 3 sin(5t)) Find the unit tangent vector T (t) at the point t = 0 T(0) = <

A:

Q: 10. r(t) = F(t) x G(t), where F(t) = t³i – tj + tk, G(t) G(t) = 3√/ti+ 1 t + īj + (t + 2) k -j 1

A:

Q: 6. Use a property of derivatives of vector valued functions to show that # [F(t) × F'(t)] = F(t) ×…

A: to show ddtrt→×rt→'=rt→×rt→'' we will use  ddtu→×v→=u→ddtv→+v→ddtu→

Q: For what values of t is the vector-valued function, 7(t) = , continuous? | Domain: {t| <t< }

A:

Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

A:

Q: In(t + 4) sin2t Given the vector valued function 7(t) = (e-3t, t a) Find the domain of 7(t). b) Find…

A:

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

A:

Q: Show that the vector-valued function shown below describes the function of a particle moving in a…

A: Part - 1 : Given vector-valued function is                                      rt = 5i +5j +3k +…

Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

A:

Q: Find a tangent vector of the curve7(t) = (t², 2 sin(t), 2 cos(t)) at (0,0, 2) (0,0,1) (1,0,0) None…

A: Here, Find it’s derivative This is the tangent at any point on the curve.