6. Derive the Hessian and find out if it is positive or negative definite. i. f(x1,*2) = 2x - 4x + 2x, – 3x3 – xx, 7 ii. f(x1, x2) =-2x1 + 4x7 – 2x, + 3x3 + x1x2

Q: Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of 2, and…

A:

Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

A:

Q: Find mzHGI.

A: Our Aim is to determine the angle HGI=?

Q: In(1+ 5.x?) 2 – 3x Differentiate with respect to x.

A:

Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: ...=AxB|^2| JĀ X B|? al . B= 2ī + 27 – 2K 3Ā = -i- 35 -k JS là

A:

Q: 2 6² 6² S (3x + 4y) 5dxdy 0 Find

A: We need to evaluate :

Q: 3. Sx³dz

A: Let I=∫x3dx1+x2.

Q: X + 3y + 2 = 10 X-2y = 2 = − 6 2x+y +2₂=10 1

A:

Q: FINO Y = L A. Y = 6x (4) Yo B. C D. Yo [2 Ge 22-x²²0 ct. 86 +38 25² +53-3 -3x 20 -3x 3x 2x [등 -2x 2…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (1 + 1)e dr 5.

A:

Q: la Graph the function f)= 2xcX -4) (xt 3] 2x(x-4)(xt3)

A: Given

Q: If (x + 1, y – 2) = (3,1), find the values of x and y.

A:

Q: S(sin2z – 3cos2z)°dz

A: Here, (sin 2z-3cos 2z)2 =sin22z-6sin 2zcos 2z+9cos22z=sin22z+cos22z-3(2sin 2zcos 2z)+8cos22z=1-3sin…

Q: If Z1=2-4i and Z2= -π+5i Find 1. (Z1+Z2) 2. (Z2-Z1) 3. (Z1-Z2)

A:

Q: Let f(x)- 3x-4 and gix)= x² +4x +5. Find f(3) = f(-2)- 9(-3): g(2): flat2): glar2)

A:

Q: 10x 9y-3z = 4

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.