For an element x of an ordered integral domain D, the absolute value Ix I is defined by                                     l xl={ x if x ≥ 0                                         {-x if o > x Prove that - lxl ≤ x ≤ lxl for all x ϵ D.

Q: Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf…

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Q: Noah invests $3,600 for two years.   The account pays 0.43% monthly compound interest. To the…

A: Given the given invest=$3,600 Interest rate=0.43%(compounded monthly) Time=2 years Apply formula…

Q: For the function Sx² - x x² – if x 1 ’ evaluate the left and right limits as x → 1.

A: We can make it easier for you.

Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Suppose I is an open interval (a, b) and f is a function defined on I which is strictly monotone…

A: Suppose I is an open interval (a, b) and f is a function defined on I which is strictly monotone…

Q: True or false: If f: (0, 1)→ R is defined by f(x)=√x for every real number a in the open interval…

A: fx=x for all real xin the open interval  0,1

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Prove that Var(E(Y|X)) ≤ Var(Y)

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Q: 5. Find values for a and b that will make f continuous everywhere, if: f(x) = Show your work. { 2x +…

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Q: Use limits to show that the function f (x) = x2 + 3 for x &lt; 1 10 − x for 1 ≤ x ≤ 2 6x + x2 for x…

A: We determine whether the function f(x) is continuous at x = 1 and x = 2.  We need to use the…

Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Let 2x - x if 0 4 (a) For each of the numbers 2, 3, and 4, dctcrmine whether g is continuous from…

A: We are given                 . For (a), For each numbers 2, 3, and 4, we need to determine whether g…

Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

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Q: Suppose that (picture) If f is  continuous for all real numbers, then c is equal to:

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Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: O is a simple zero of f(x)= secx+e2 -2 %3D Select one: True O False

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Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) &gt; 2      if 0&lt;=X &lt; 1.Is…

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Q: Let A =[1 -1]            [2 0] and --->x =[ i]                  [1 + i] . SHOW that Re (A--->x )…

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Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

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Q: Find the absolute minimums and maximums of the following function on the given intervals

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.