1. Exercise. Suppose p : R → R° and q :R → R° are vector-valued functions. Further assume p'(-1) = (1,2, 3) and q'(-1) = (1,1,-2). Let v(t) = p(t) + q(t) be yet another vector-valued function. Then v'(-1) = Exercise. Let f(t) = (1,2,3). Find v(t) so that v(0) = (0,0,0) and v'(t) = f(t). v(t) = Exercise. A curve C is described by the vector-valued function p(t) = (t², 4 – 2t2, t2 + 2). Exercise. Find all t-values where p and p' are orthogonal. List your answers in order from least to greatest: t = t = t =

Q: Given r(t) be a vector function that satisfies: r'(1)= T'(1)= 1) Determine the unit tangent…

A: Given, r'(1)=<-3,0,4> T'(1)=<2,2,1>

Q: 5. Consider the vector-valued function R(t) = (t³ — t, 2t², 2 — 2t²) a. Find ||R'(t)|| (Simplify…

A:

Q: C

A:

Q: The smooth vector-valued function P(t) satisfies P(2)= (-4, 8,-7), P′(2)= (0,-5,2), and P'(2)= (3,…

A:

Q: Let ß be the vector-valued function 3u B(u, v) = { 32 ß: (-2, 2) × (0, 2π) → R³, 3u² + 4 COS(V) } u…

A: Since you have asked multiple questions, we will answer the questions (a) and (b) for you. If you…

Q: Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) =…

A: rt=et,e2t,t0=0

Q: 2.31 Let A and B be vector functions of position vector x with continuous first and second…

A: Let A and B be vector functions of position vector x with continuous first and second derivatives,…

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: In this question , we have to find out velocity vector, speed and accleration vector from position…

Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

A:

Q: 2. Consider the vector-valued function R(t) with Ả(1) = (1,2,−1) and R'(t): = (17/3/7-2) a) Find…

A: According to the guideline, only three subparts of the question can be answered. Please repost other…

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Consider the function f(x,y) = 3- a. Fill in the table with the values of the directional derivative…

A: Here to find the directional derivative at (a, b) of fin(x, y) the direction of unit vector u, v and…

Q: II. Let F and G be vector-valued F(1) = (1,0,2), F'(1) = (1,1,2), G(1) = (2,1,3), G'(1) = (-1,…

A:

Q: Find a equation vector and the equation of the tangent line at the point P0 where t=0.2 on the graph…

A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = 3 cos(t)i + 3 sin(t)j, to r'(t) =…

A: The given vector valued function

Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

Q: 2 Consider the vector-valued function R(t) with Ả'(t) = (sec²(t – 1), √t' (a) Find R(t) given Ả(1) =…

A: a) Given: R'→t=sec2t-1, 2t, -2 and R→1=1, 0, -1 To find: R→t

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

A:

Q: t) = (et, e24), to = 0 لاخت لا rve represented by the vector-valued function, and sketch the vectors…

A: