1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C) %3D

Q: (12) Find the Value of b such that: [3x² dx = 27 (A) 6 (C) 9 (B) 3 (D) none of these 4

A: Step 1:To find the value of b such that ∫0b​3x2dx=27, we need to solve the definite integral: Step…

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: Find (f g)(x). f(x) = 7x + 9, g(x) = 4x - 1; A) 28x + 8 B) 28x + 16 C) 28x + 2 DJ 28x + 35 op

A: The given functions are  f(x) = 7x +9 g(x) = 4x - 1 To find (fog)(x)

Q: Find A. C. d³y dx³ given y = 48(x²-3) (x² + 3)4 24x(x²-3) (x² + 3)4 2 x²-3 B. D. -48x(x²+3) (x²-3)4…

A:

Q: If fx) x) f(1) = and f(1) -2, find 1) -16/13

A: Formula used:

Q: A = {x € Rx ≥ 5 and x 8 and r < 12}

A:

Q: | (x - i) i=-1

A:

Q: Evaluate: 3 f(-x² + 4x-1)dx 1

A:

Q: f. f(t) = eat cos² b t.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Find f'(1) if Ax) = (4x- 3) %3D 2.

A:

Q: Evaluate: (x + 6)(x – 5) dæ + C

A: We will solve the problem

Q: 7k +5)dx t

A:

Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

A: Given that: (b) y=exx2(c) y=cosx2+1(d) y=2x2x+1 The quotient rule of derivative is…