3 L[y] =y' --y is a linear operator. If u(x) = −4x² + 2x, then find L[u(x)]. X a) -4x² - 6x b) - 12x³ 6 c) -4x³ - 4x d) -4x³ 4 -4x² 4 f) None of the above.

Q: conjugate of v-1-3 is 1- V-1+3 2- -V-1-3 -V-1+ 3 3 - V-1 2- 4-

A:

Q: Find y' if y= 48x³+34x2-8x+15 (4x-1)² 48x³+34x²-8x+33 (4x-1)² If y = 3u² - 2u + 4 and u = x² + 3x -…

A:

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

A:

Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: x2 + 2y2 + 3z2 = 1

A:

Q: 1. (2u). (2v) = 2 (u.v) 2. (7x+3y). (6x + 4y) = Note: u. (vw) = u(v + (−1)w) =u.v+u.(-1)w =u.v +…

A:

Q: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: 2) g(x)= -2 () 2x+1 Transformations: a= b= h= k=

A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

Q: The solution to (2x+5)= -(x+2) lies on which interva а. [-12,-8] 2. 15 b. [-9,-4] c. [-3,-1] С. d.…

A: Given  115 (2x+5) = 19 (x+2)⇒ 93 (2x+5) = 155 (x+2)⇒ 3 (2x+5) = 5 (x+2)

Q: 3. y = (x+b)(x-a). (x-b) ; y

A: A detailed solution is given below. Use logarithmic differential to solve it.

Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

Q: 6y" – y' – y = 0

A:

Q: 1. Given the algebraic function x² xy + y² = 3

A:

Q: Which of the following operators in R'are linear? 1. T(x) = (8x2, -5x, -9x) %3D 2 T(x) = (10x; - 7x2…

A:

Q: Find x, y, z, and w. X = y = Z= W = x 7 (2x y 6 - 5) (2x = ¹) ] - [ (²x - ² 9y Z 9 By + 8) ] 8 (w +…

A:

Q: 3(z+9)=

A: 3(z+9)=3z+9×3 By simplify the equation by open the bracket

Q: y)(Ty → Wy) - Hv)) → Ia

A:

Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

A:

Q: 2. Let -2 3] 1 5 A = (a) Write down the quadratic form, Q(x), for AT A.

A:

Q: i= (hxz ¹hize + ₂x¹x + h_) ×A

A: