a. Show that F(x) is given by Fs(x) = 0 (i) Pr(S≤ 0.5) (ii) Pr(S≤ 1.0) (iii) Pr(S≤ 1.5). x³ - 3(x - 1)³ 6 x³ − 3(x − 1)³ + 3(x − 2)³ 6 1 x < 0 0≤x<1 1

Q: 3. Which one of the following statements is CORRECT? A. ff(x) dx + f(x) dx = 0 B. ff(x) dx-f(x) dx =…

A: These statements are related to properties of integration. Here, We will use some integration…

Q: Q.12 Find f(x), if Js(n) = 16(-1)-1 n 0<x<8

A: Given: Let us consider the given data, f¯sn=16-1n-1n3,0&lt;x&lt;8 To determine: fx.

Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sin x, determine (fog)(x) and (fog)(2), 0≤x≤ 2n.

A:

Q: Given the defined function f(x) 2x +8, x 3

A: Explanation of the solution is given below...

Q: 5. For what value of the constant c is the function f continuous on (-0, 0) < f(x) = {cx²-20 [cx²-2c…

A:

Q: 4. Find the f(x) = = value of the constant b for which f is continuous at x = -1 and determine…

A:

Q: 46. If f(r) = 2ur +|r – 2| – ||| and 0 < z < 2, then S(z) = A 2 B 2+ 4x C 2-4r D -2+ 2x 2 –

A: Given that fx=2x+x-2-x with 0≤x&lt;2. Since 0≤x&lt;2, we have  x-2&lt;0 and  x≥0. Now,…

Q: It is given that g (x) = 2x – 1 and h(x) = g(2x-1). %3D (a) Express h(x) in terms of x. (b) If g(p-…

A: Given: g(x)=2x−1h(x)=g(2x−1)

Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sinx, determine (fog)(x) and (fog) (), 0≤x≤ 2n.

A:

Q: 6. Suppose f(x)-<ɛ. Solve for|x-1 where f defined below. x 1 f(x) = 2 3

A:

Q: 11. For what values of "a" and b is the function is continuous at.x31 f(x) = ( 3ax +b: x>1 %3D 11:…

A: A function f(x) will be continuous at a point a if:   limx→a-f(x) = f(a) = limx→a+f(x)

Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

A:

Q: ef f(² Evaluate √ ² f(x) f(x) dx, where f(x) dx = f(x) = (5x8, 0<x< 1 4x4, 1<x<2.

A:

Q: 24. Find the constants a and b such that the function below is continuous at x = 0 and x = 1 1 - x²,…

A:

Q: 3. Determine the values of a and b if the given function f(x) is continuous. (2x + 6 ,x 2 Solution:

A:

Q: 1.lf f(x) =x2 – 2x – 1, find f(-2). |

A: We have to find f-2 when function is given as: fx=x2-2x-1 In this case we just have to put the…

Q: /Find f(x) , identify the domain & range of f(x), then show that f(F"(x) = f"(F(x)) = x for the…

A:

Q: Evaluate L{f(t)} for f(t) = 0, 0 ≤t<3 2, t23

A: We have to evaluate .

Q: 1 Let f(x) and g(x) = 3x + 7. 4 - Then (f o g)(3) (f o g)(x) =

A: This is an example of composition of function. Put the function g in f intended of x for fog(x)

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: 10x Let f(x)=108-9x 58 2 if x 6 if x=6 Is f(x) continuous at x = = 6? Yes O No Cannot Be Determined

A:

Q: If 12 ≤ f(x) ≤ 18, then O≤ ≤[ f(x)dx 2

A: Given: 12≤f(x)≤18 We are required to fill the blanks: ≤∫29f(x)dx≤

Q: 10 Find f(x) dx if f(x) = [8 for x< 8 |x for x 2 8

A:

Q: 7. Find the value of K that makes the function f(x) = (x² + 2 , x > 5 (x² – xk – 3 , x< 5 Continuous…

A:

Q: 1. What are the critical values of f(x) = -8x-x² +

A: On solving this we will get

Q: 16. Find the value of the constant k so that the function f(x) = { kx-5 if 0 < x < 2; is continuous.

A: We are given a piecewise function and we need to find out the value of the constant k such that the…