Q.3. Let X = (a, b, c), T= (X, . (a), (b.c}), Y (1,2, 3), r (Y, . (1), (1,2)} and a function f:X-Y where f(a) = f(b) = 1, f(c) = 2 are given. Discuss if f is open or continuous ?

Q: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). Which of the…

A: Given: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). To Find:…

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A: Domain.

Q: Theorem 7. Let X be a continuous RV, g a function from R to R. Let Y = g(X). Then E[Y] = E[g(X)] = /…

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Q: 5.(10 pts) Find an analytic function f(2) = u(x,y) + iv(x, y) such that u(x, y) = x² – y? + 2. Write…

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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Q: Consider the function d: R² × R² → R defined by {} d(x, y) = min{|y2x₂, 1} if x₁ = y₁ otherwise, 1…

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Q: 6. Let F(x, y) = (y, x). Find a function f (x, y) such that Vf = F. %3D

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Q: 8. Consider the set f = {(x, y) E Z xZ:x+3y = 4}. Is this a function from Z to Z? Explain. %3D %3D

A: 8) Given the set, f=x,y∈ℤ×ℤ: x+3y=4 No, this function is not from ℤ to ℤ Explicitly writing the…

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Q: (b) A continuous function f : [0, 1] → R such that its graph (r, f (x)) C R² is not closed.

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Q: Show that a function f : R? → R defined by S (7, y) = ! if (x, y) + (0,0) 0, if x = y = 0 is…

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Q: 3. Describe the interval(s) on which the function is continuous. c) S(x)= x-1 2, x= 1

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Q: f(ix, λγ) - λκ. f(x, y)

A: Given: fλx,λy=λkfx,y

Q: Show that if w = ƒ(s) is any differentiable function of s and ifs = y + 5x, then∂w/∂x - 5 ∂w/∂y = 0

A:

Q: 1. Find if the function is continuous in the given points A) f(x, y) = B) f(x, y) = xy √x² + y² 0…

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Q: 2. The function y= fx) is continuous on its domain and some function values are given in a table…

A: Solution Given:-               x         1         2        4      6       y       0.1…

Q: Let f(x) = ()*)**, x = 0,1, is p.d.f then P(x = 0) = %3D

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Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: 3. Consider the set f = {(x,y) E Z × Z|3x + y = 4}. Is this a function from Z x Z.

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Q: Suppose f, g:C → C are differentiable. Prove that fg is differentiable and that (fg)' = f'g + fg'.

A:

Q: 2.) Determine the set of points at which the function is continuous. а. F(x,у) — 1+x²+y² 1-x2-у? ху…

A: Here, to find the set of points at which the function is continous.

Q: (1) Suppose f: [a,b] → [a,b] is a continuous function. Prove that there exists a cE [a, b] such that…

A:

Q: If f is continuous on [-1, 1] and f(x)dx = 0, then there exists some ce [-1,1] for which f(c) = 0.

A: Given: f is a continuous function on the interval -1, 1 and ∫-11f(x) dx=0. Prove: There exists some…

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A: Suppose fand gare two continuous functions on [a, b] and f(a) <g(a) but  f(b) >g(b).  Show…

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Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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Q: Which of the following is the domain set of the function f(x,y)=arccos(x² +y² -3)+In(x² + y² -3) ? =…

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Q: 2. Determine the points where f is continuous where x + Y if (x, y) # (0,0) f(x, y) = x2 + y2 if (x,…

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Q: If a function f is not differentiable at x = a E R, then f is not a differentiable function. True O…

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Q: (3) Determine the values of a for which x4 + y* , if(x, y) # (0, 0), (x² + y?)ª f(x, y) = ,if(x, y)…

A: solution.

Q: 7. Find a and b such that f is differentiable everywhere. f(x) = {+b, S ax³, lx² + b, x 4

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Q: Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the…

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Q: show that F(X<1|Y<y) + P(X <1) for some z, y.

A: dependent events:  Two or more events are said to be dependent if occurrence of one affects the…

Q: Let f(x, y, λ) = xy + λ(5 - x - y). Find f(1, 2, 3).

A: Given : fx,y,λ = xy + λ5 -x -y

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Q: I. Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y…

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Q: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: 7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e.,…

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Q: Let X and Y be t function discrete ran X--1 1, 2. y-4, 9 27 P(x, y)- 0.

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Q: Find and for the functions: of Əx af ду bren 2. f(x, y) = x² − xy + y² X (x² + ² noitonut sil 4.…

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Q: Which of the following statements is true about a smooth function f at (a, b) if ƒ (a, b) = c, fæx…

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Q: 1. If g(x) is a continuous function on [2 ,9] such that , g(x)dx = 25 and ,9(x)dx = Find value of…

A: Using the properties of definite integral, it can be written as follows.

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

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Q: 1. Show that if u = x – y, v = y, then for any continuous function f, -" f(r – y, y)dydæ e=s(u+v)…

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Q: Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y is…

A: Given function is fx,y=1,           x,y=1,−1x2+yx+y  ,x,y≠1,−1 . We have to show that the given…

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

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Q: 5) Suppose a path C is defined by r(t), 2 and r(8) = . If f is a differentiable function satisfying…

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Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

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