2. Prove or give a counterexample to • If X ≤Y then Var (X) < Var(Y) • Var(X-c) < Var (X + c) for c>0 . Var (X) ≤ Var(X)

Q: 2. Determine all values of x for which 0<= x2-11/x+1<=7 (include graph and intervals tables) *in…

A:

Q: x+ 6x +7 f(x) = {-x + 3 5 if x < -1 if -1<x<3 if x 2 3 f(2) = %3D f(-1) = S(-7) = S(3) =

A: The given step function is f(x)=x2+6x+7if x&lt;-1-x+3if -1≤x&lt;35if x≥3

Q: The function f is continuous on the interval -2 < x < 5 and is not continuous on the interval -2 ≤ x…

A: The function  is continuous on the interval and is not continuous on the interval . To find the…

Q: (a) Show that the following sentence ¬Vz(3yR(x,y) = R(x, f(x, x)) is satisfiable where f is a…

A: a)

Q: For all x, there exists y such that (y^2 <= x <(y+1)^2) when domain is N(natural number) I want to…

A: For all x, there exists a y, such that,  y2 ≤ x &lt; (y + 1)2   Given that x is a natural number,…

Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

A:

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: LET b₂= SHOW THAT faxi) - faxo). (x₂-xo) f (x₂) - fcxo)_ _faxi) - faxo) (x₂-x₁) (x₂-x₁) (X₁-Xo)…

A:

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

Q: There are true statements of f(x) = 5(x4 – 4x³) , except ... Pernyataan yang salah mengenai kurva…

A:

Q: (0 < * < 1) (-1<* < 0) (4) If f(x) = %3D expand f(x) in the form c,P,(x).

A: Give that: f(x)=-12, -1&lt;x&lt;012,0&lt;x&lt;1  Here L=(1+1)/2=1 Fourier  series expansion given by…

Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

A:

Q: ²-8 If f(x) = X-4' X = where is f not differentiable?

A:

Q: Find the domain of f(x)= Mostly sunny x|x€Rx‡¬ √10} 00 x|x€R_x#√10} Ox|x€R¸x*-√√10, 10}…

A: a2 - b2 = (a - b)(a + b)  and 10 = (10)1/2(10)1/2

Q: Consider the function f(x) = 4x² - 4x4.

A: Given, f(x)=4x2-4x4

Q: VxVx2((f(x1) = f(x2)) → (x1 = x2)) O composite O injective O surjective O bijective

A:

Q: What is true about the function f(x)= = a) f(x) → from above b) f(x) →2 from above c) f(x) → from…

A:

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: f(x) = - 4x+5 if -1<x<2 3x-8 if 2≤x≤4 The domain of the piecewise defined function fis [-1,2]U[2,4]

A: Given a piece wise function

Q: Which equation matches the graph of the piecewise function f(x) below?

A: Given,

Q: how many critical numbers does the funtion f ( x ) = | x 2 − 5 | have?

A: The graph of the function given below.

Q: 00 ak 10. If f(x) = ar(x - 3)* for all real r, then the function F(r) = (-3)*+1 has %3D k=0 k+ 1 k=0…

A:

Q: 4. Which ones of the following functions are valid CDFs (all have x ≥ 0): (b) 1-exp(-) (0)1-exp(-)…

A: We are given the set of cumulative distribution functions .We have to choose which of the given…

Q: 23) If f: IR→IR and g: IR^ IR are continous, show that the functions f²g: IR^ → IR₁ × → [fos]ªg(x)…

A:

Q: What is the domain of x↦ (1)/(x^(2-25)) ? b. Explore x-> (1)/(x-|x|) to determine what inputs, if…

A:

Q: 4a) Find the x-values (if any) at which x²+x-12 f(x)= x-3 is not continuous. 4b) If there are any…

A:

Q: Find the extreme values of f(x) = In 1+x SOUITION

A: Given- fx=lnx1+x2 To find- The extreme value of the above function.

Q: Let i, j ∈ Za and w, x ∈ Zb with i, j different from each other and w, x different from each other.…

A: Say, the total number of elements in Za = m, the total number of elements in Zb = n,  The total…

Q: Let f(x) = -x4-9x³+2x+8. Find the open intervals on which is concave up (down). Then determine the…

A: For a given function f( x ) ( a ) inflection points by f''( x ) = 0 ( b ) For concave up , f''( x )…

Q: Suppose that To (2) centered at 3 for f(x)is given by Ts (2) = 7+3(2-3) + 2(x-3)² + 4(x-3)³ + (x-3)5…

A: Given that , T6x=7+3x-3+2x-32+4x-33+x-35+5x-36 and T6x centered at 3.

Q: A17 Let Xx² (99). What is Var(X)? Answer to A17:

A: X~chi square (99) We have to find var(X)

Q: Define f(x) = {x2 if x ≤ 2                        5x > 2}  Find each of the following.  a) f(1) b)…

A: Function is given, if x is greater than or equal to 2 then the definition of the function is f(x)=x²…