(a) X (b) X (c) X E X-μ (d) (n-1)s² (e) X1+Xn 2

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: Which is true for the f (x)= (2x-4x)e A. f(x)=e* B. f(x)=e*-1 C. f(x)=e D. f(x)=e

A:

Q: Given 3 fºF f(x) dx = 4 and [FO f(x) dx = -1, evaluate the following.

A:

Q: Show that (a) x(t) * 8(t) = x(t)

A:

Q: If f f(x) dx = 6, f f(x) dx = 2, and f, g(x) = -5, find f₁[2f(x) — 4g(x)]dx.

A:

Q: E(X)=5 and E(Y)=8 What is E(X+4Y)?

A: From the properties of expectation:-EaX+bY=aEX+bEY

Q: –1/2 | (x (x² + x) + 4)dx.

A: Given,            ∫04x-1/2x2 + x + 4 dx

Q: 1. g(x) (x - 4)2/2

A: Find g’(x) and equate to 0 to find the critical point.

Q: (c) [6 pts] In(x + 1) In(1 - x) = 2. I (d) [7 pts] 2.31-2x = 7.64+x

A: Question cx = 0 and 3 Question dx=−3ln(3)+ln(2)3ln(2)+3ln(3)+ln(7)​≈−1.835Another way of expressing…

Q: C. Çompute (f.g)(x) and (g.f)(x) for f(x) = 4x – 1, g(x) = v6 + 7x %3D %3D

A:

Q: Using Rodrigues' formula for Pn(x), (T) (i) Pn(-x) = (-1)" P₂(x) cl

A:

Q: If g(x) = x3 and h(n) = 4n − √(n), what is (h ◦ g)?

A: g(x)=x3h(n)=4n-n

Q: (c) f(x) = e² – x + In(x) %3D

A:

Q: (3 − |x|)dr is equal to L (3 (a) f( (3 - x) dx (b) [(3+z)dz (c) [²₁ (3 - x) dx + [² (3 + x) dx (d)…

A:

Q: Given √,³ 0-12 f(x)dx = 8 and g(x)dx=-4, what is -4 4 12 √,³ (g(x) − f(x)]dx?

A:

Q: (iv) S: (1-x²)z dx x8

A: Given:

Q: Find (x + 2)(x-7)dx (x + 2)(x − 7)dx= + C

A:

Q: (9) If f(x) = 2x +k and g(x) = (x – 5)/2, for what value of k is f(g(x)) = g(f(x))? %3D (A) 15 (B) 5…

A: