Let f : R" → R be a function. Consider the converse proposition of (6.1) given below: If La(f) is a convex set for each a E R, then f is a one-to-one function.

Q: L{f(t – a)u(t – a)} = e¬as F(s) |

A: Topic:- Laplace transform and it's properties

Q: - (7)f | dt, then f (z) 1.

A:

Q: Integrate: +C 16t6 t4 [√16 dt

A:

Q: (part 1 of 4) Determine fa- fy when 1. 2. 3. 4. 6. f(x, y) = 4x² + 4xy - 4y² + x + 2y. fx-fy = 12x -…

A: Topic = Derivative

Q: (9) IfX~F(ri,r2), then оо От OF rix 12 1+1x 12 ~Beta (z, z).

A: False

Q: evaluate using the appropriate method or combination of methods.

A:

Q: Show that f(z) = Re(z) = x is not differentiable at any z. W 20

A:

Q: Suppose that f: [1,9] →→ R² such that f(1) =(2,-2) and f' (t) Find f(9) (v₁, 71) √t, √t

A:

Q: For æ > 0, 1 dt 1+t2 A 2/7(1+z) B 2/7(1+JE) c) 1+1 D 1+z E VE

A:

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

A:

Q: T: M22 --->M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---> M2×2. We have to find the…

Q: Is F = (3x² - 4xy, 2x²) conservative? If so, find a potential function. Support your answer.

A: Here we have to find whether F is conservative or not. If it is conservative then we have to find…