please find the solution of x(t), given dx/dt = Ax(t) with A=[[1,-1],[1,3]] and x(0) = [5,-7]T

Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

A:

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

A:

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

A:

Q: Determine which of the following pairs of functions are linearly independent. 1. f(t) = 3t, g(t) =…

A:

Q: The derivative of y= (V x - 2 )(Vx+1) is equal to: х - 1 A 2x+1/x-2 2х-1 B Jx+1/x=2 2х-2 2/x+1/x-2 D…

A:

Q: Find f(x), if f(x)=f(x)+ƒ f(x) dx, given that f(0) = 1.

A:

Q: Show human working correctly please

A: To find f'(1), we need to differentiate the given function f(p) with respect to p and then evaluate…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

A:

Q: = f²³² € 0 Given F(x) = -t² e dt, use FTC Part II to find F'(1)

A:

Q: Find the linear approximation L(x) of the function ¹ƒ(x) = x² + 2x³ at a = -1.

A:

Q: Let X1, X2, X3 and X4 be a random sample from population with pdf 0 < x < 1 X, fx(x) = 0, otherwise.…

A:

Q: Find the values of the coefficients a, b and c so that the conditions f(0) = 1, f'(0) = -10, and…

A:

Q: Let g'(x) 0. B. g(1) = - 3, g(7) = 1, g(15) = 10 1 C. g(1) = 1, g(7) = 7, g(15) = 14 D. g(1) = 10,…

A:

Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

A:

Q: Evaluate ∫03 (4f(t)−6g(t)) dt given that ∫015 f(t) dt=−7,  ∫03 f(t) dt=−8,   ∫015 g(t) dt=4, and…

A: We use the property of definite integral shown on board.