Find all critical points of the given plane autonomous system. (Enter your answers as a comma-separated list.) = x( 14 - x - — /v) (x, y) = x' y' = y(24 - y - x) 0,0, 0,24, 14,0,

Q: 5c) Find the partial derivatives?     y = 2x2+3xz+85w-8z2

A:

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: f(x, y, z) = x-y y²+2y+z²-4

A: We have shown that the domain is all of R3 except the points on the surface of infinite length…

Q: F .2 .2 x- +y at A=(2, 3), B=(-2, 2) and C=(3, -4).

A: 1.) div F at A(2,3) = <4,6>2.) div F at B(-2,2) = <-4,4>3.) div F at C(3,-4) =…

Q: Q5) Find the coefficients a, b, c and d such that the curve defined by; y = ax³ + bx² + cx + d,…

A: Given: The curve y=ax3+bx2+cx+d passes through the points 0, 10, 1, 7, 3, -11, 4, -14. To find: The…

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: Calculate fx (1, 3) and fy (1, 3) for f (x, y) = √(7x + y^2).

A: For a function of two variables, partial derivative with respect to one variable is calculated by…

Q: Find a parameterization for a line passing through the points (1,1) and (5, 13) O x = t, y = 3t-2 O…

A:

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: Find f(1, 3) and f,(1, 3) for the function f(x, y) = 2x'y² + 2y +4x.

A: Given function is f(x,y)=2x3y2+2y+4x find fx1,3 and fy1,3

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Find the domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for…

A:

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin (t). Find af af and (write your…

A:

Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

A:

Q: What do you mean by asymptotically stable for autonomous equations ?

A: Given: asymptotically stale for autonomous equation A critical point x∘ of an autonomous system is…

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2