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: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

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Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)&gt;0 when…

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: Let X have a p.d.f. fx(x) = {} -1 < x < 2, otherwise. Find the p.d.f. of Y = X².

A: Given X have a p.d.f and Y=

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) Let M = R. Give the radius r and the center c of B(-2,5) n B(6, 7). ne

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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

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Q: y + 2xy). Find values of a and b so that f (x + iy) will be analytic. Consider the complex-valued…

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Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

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Q: 12. Let g(x, y) = V36 – 9x² – 4y². (a) Evaluate g(1, 2). (b) Find and sketch the domain of g. (c)…

A: Range and domain of the function

Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

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: x* +1 a Which of the following is not an asymptote of the curve. 3 - f(x) = - (x² –1)(x² – 4) O A)…

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Q: Find the (natural) domain of the function x + 1 2х — 1 f (x) = Select one: a. (-0, –1] U (1/2, ∞) b.…

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

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Q: Q.: Find the radius oP- and the interva l Co nvergence of Gnvergen ce (x-2)" Incn+4)

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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: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

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Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: 2. Let g(x) = [x]. Find: 2.a g ¹({0}) 2.b g¹({-1,0,1}) 2.c g ¹({x 10 < x < 1}).

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

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

Q: 2 + v - , 2+z+ 11. 0. di

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Q: z? f(2) = 1-z* 4

A: We use the fact that the 1/(1-z)= 1+z+z2+z3+z4+......

Q: Let f(æ) = /90 - x and g(x) = x² – a. Then the domain of f o gis equal to [a, b] for a = Preview and…

A: Given: fx=90-x, gx=x2-x

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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Q: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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