Let o be the hypercube [0, 1]". For any f e C[0, 1] show that (). (x1 + x2 + + Xn dxjdx2 dxn = f ... lim n-00 n

Q: Q: Interpret the vate of change f y = (-2 Jn=+1 + 5) (45 -2) with Yespect to

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Q: Give an explicit increasing linear bijection from the interval (a, b] (a < b) to (0, 1]. i.e. your…

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Q: 3. Let d= = [( ) ( ) ( ) ( )], B = [1, 2, 2²), v = (¹). " (a) If f(x)=x²-3x+2, compute [ƒ(x)]ß. -1 2…

A: Our objective is given below:

Q: Q[V5]is Principal Ideal Domain. True False O O

A: If Q5 is a field, then it will be principle ideal domain. It suffices to show that every element of…

Q: Verify that fxy = fyx for the following funtion.  f(x,y) = ex + y + 1 fxy = ? fyx = ?

A: Given,            fx,y=ex+y+1

Q: .A. Find the domain of the tollowling Fune tions :- 1. Fex) = V4-12X

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 20xth)t xth 3. Zx- Find the limi,t

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Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

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Q: (d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.

A: We will use the vector/matrix notations to visualise things easily.

Q: INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→ R-{} defined by f(x) 3x-5 = is bijective. 2x+1

A: Given :  f: ℝ--12→ℝ-32   defined by ;                f(x) = 3x-52x+1 To prove : f is bijective.

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: Sketch the groph of the funchion and find domains range x+3. if x L-3 and continuity of Hes (x)<x2…

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Q: A. Find the domain and range of А. f, g,f + g, and f • g following: of the 1. f(x) 3 х; g(x) = Vx –…

A: Domain = the set of values of x for which the function is defined. Range = the set of output values…

Q: What is true about the function -- asx-m? OAM-f B) (x) 0 from below OC) f(x) is undefined OD)x) from…

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Q: Let f be the function defined by f (x) = x³ – x² – 6x. What is the absolute maximum value of f on…

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Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

A: If the function is injective , then the above statement is true.

Q: Find the. Lo. T.of the non-peridic functon= oくtく」 f(t) =

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Q: f. Is the domain of f(x.y)= In (6x + 5y“) bounded or unbounded? O Unbounded O Bounded

A: the domain will be Unbounded because

Q: Let X = R – {2} and Y = R – {3}, where R is the set of real numbers. Show that Card(X) = Card(Y).…

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Q: 1. Find the value of c to make the following piecewise function continuous on the the interval (-o,…

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Q: I Consiter Hhe follwing pdf: PxY (xy). -2 di) Find Px and Px e) Find Pxir (xly) for every y. fo)…

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Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

Q: If possible make an explicit bijection from [0, 1] to [-2, -∞. If no possible, Why? If…

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Q: Differentiate: f(x) = 4x³ - (5/x²) %3D O a. f(x) = 12x2 - (10/x³) O b. f(x) = 12x2+ (10/x³) O c.…

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Q: . Consider f(2)= (+ i)¹/3. Choose a set of branch cut (s) and sketch it in the complex plane. For…

A: As per the question we are given a complex function as : f(z) = (1/z + i)1/3 And we have to choose a…

Q: What is the Vertical Asymptote of the function

A: Given: f(x)=4xx+3

Q: 3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R,…

A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

Q: The domain of the function f(x) = arccos(√3x²-2) is: O A. all x in the interval [¹]. O B. all x in…

A: we need to find the domain of the given function.

Q: ( 82) Ex: Find the Faurier exfansionof fex+

A: The Fourier series of given function is given as follows :

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: k 1. Prove that \k

A: In the first part, it is required to prove that knnk=n−1k−1 We know that nk=n!k!n−k! Now take Left…

Q: verify 'If yes, explain why. If no, provide a counterexample. the following statement. For every…

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Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: Let frx) = (x²+2x), and g(4)=(1++) find gof and f.g.

A: Given, fx=x2+2x and gx=1+1x.   The objective is to find g∘f and f∘g.   g∘f is found as follows:…

Q: - a) Write the function f(t) uc(t). = t, -t+4, 0, 0<t<2 2≤ t < 4 by using step functions t24

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Q: This problem is about giving an example of a function from Z to Z that is onto, but not one-to-one.…

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