The smooth vector-valued function P(t) satisfies P(2)= (−4, 8,−7), P′(2)= (0,-5,2), and P’’(2)= (3, 1, −6). 1. Look for a vector equation of the tangent line to the graph of P(t) at t=2.

Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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: (a) Find the direction for which the directional derivative of the function f(x, y, z) = √√x² + y² +…

A:

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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: You are given the derivative of a vector function r in the component form is dr (e,3e",-2t). You are…

A: Given that: drdt=&lt;e-t, 3e3t, -2t&gt;          and r(0)=2i-j+k

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: Let 7 (t) = (4t³ – 4, – 3e", – 3 sin( – 4t)) - Find the unit tangent vector T(t) at the point t = 0…

A:

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

A:

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: Find the domain of the vector function. lim t->infinity

A: Answer

Q: Find the velocity vector v(t) and the acceleration vector a(t) of the straight line motion given by…

A: Consider the given question,The velocity vector v(t) from the given position vector is find as,

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

A:

Q: 4t Let (t) = ( - t +2, -3e-4, -5 sin( - 2t)) t¹ Find the unit tangent vector T (t) at the point t =…

A: