It is sufficient to give the correct answer. a) Someone asks you to study a function f (r) for small input vectors r. What should be your first reaction? b) Give an example of a parameterized curve r(t) = (x(t), y(t)) such that t r(0) = (0, 1), r(1) = (1, 2), |r' ( 1/2 )|= v2 c) Enter a continuous function f (x, y) that is not derivable at the point (0, 1) and has a local minimum with the value 2 at this point

Q: 4. (a) Determine the directional derivative of f(x, y, z) = zety at the point (1, −1, 1) in the…

A:

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: The curve C is defined by the function,on the interval,The length of the curve on the given interval…

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

A:

Q: "ind the family or vector-valued functions whose second derivatives dt² (-2 cos(t), 6). (Your inst…

A: Answer given below.

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

A:

Q: Eliminate the and write an equation of- carve in part (a) Sobely in cartesian coordinates x, y (e)…

A: As asked we shall solve only part (d) and (e).We have to eliminate the variable t and write the…

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: 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

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.