Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given by x (0) find the the functions #1 (t) and x2(t). Enter your answer as a 2x1 column vector, i.e x2 (t).

What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?

Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect.  Please Provide Unique Answer. Thank you!

What is the velocity​ vector?

2.30 Let r denote a position vector r = x = xiêį (r² = x₂x₁) and A be an arbitrary constant vector. Use index notation to show that: (a) (c) ² (r) = n(n+1) rn-2. V. (rx A) = 0. (b) (d) V(r. A) = A. ▼x (rx A) = -2A.

Find the values of x and y for which (x + y, 0) = (3,1 - y)

Consider the linearizable functions as follows. Find new transformed variables (x, y, B or B as you need) to linearize the functions below. 21 y= Biz1+ Bo.

h(x1,x2)=x2e-x1 at (2,-1)

(3) Suppose that the position function of a particle moving on a coordinate line is given by s(t) = ³-2t² + 3t - 7 in meters, where t is in seconds. (a) Find the velocity and acceleration functions; (b) Analyze the direction of the motion that shows when the particle is stopped, when it is moving forward and/or backward; (c) Analyze the change of speed that shows when it is speeding up and/or slowing down; (d) Find the total distance traveled by the particle from time t = 0 to t = 6 seconds.