Let A = {x, y} and B = {w,z}. Describe all relations from A to B. Indicate which of these are functions.

Q: Let be a derivable function and h '(x) = g (x2 +1). Calculate h '(1) if g' (2) = 5.

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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Q: Let F: X Y and G:

A: Given: Let F : X→Y and G : Y→Z be the two non-constant holomorphic maps between Reimann surfaces.

Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: Determine whether z is a function of x and y. xz2 + 2xy − y2 = 4

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Q: Let f(x) be a twice differentiable function with f(1) = 2, f(4) = 7, f'(1) 5 and %3D f'(4) = 3.…

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Q: Let be a derivable function and h (x) = g (x2 +1). Calculate h '(1) if g' (2) = 5.

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Q: Differentiate the function.

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Q: Let f(x) = x², g(x) = 2" , and h(x) = sin x.

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Q: Derive the autocorrelation function of: x₁ = $xt-1 + εt + 0€t-1 assuming that p < 1, and E(?) = 0²,…

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Q: Express the function in the form f•g•h. 45. R(x) = Wx – 1 46. H(x) = /2 + |x| 47. H(x) = sec*(/r) =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X= {a,b} and Y={1,2,3}. Find the number n of functions from X into B

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Q: Suppose utility function takes the following form: uz = u(c¿, m,, l;) = (c;m¿)'l&.

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Q: Show that the following function is nowhere analytic. f(2) = 2xy + i(x² – y³) %3D

A: Function is said to be analytic at a point if there is a nbd of the point such that f is…

Q: Differentiate the following function. r(t) = (7t,16/t, ,16/E, r'(t) = OOD

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Assume that f(x) and g(x) are both differentiable functions. Given f(3) = -2, %3D g(3) = -4, f'(3) =…

A: f(x) and g(x) are both differentiable functionf(3)=-2, g(3)=-4, f'(3)=8 and g'(3)=2h(x)=3f(x)g(x)+2

Q: Differentiate the function. z(y) = A/y12+Bey

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Q: Let f : R → R be a function given by f(x) = 2x – 1 (a) Determine whether f is bijective or not. (b)…

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Q: Assume that g(x, y) is a function of the form x² + y² g(x, y) = 0 (i) Show that if (x, y) = (0,0),…

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Q: Define a relation M from R to R as follows: For all real numbers x and y, (x, y) E M means that y =…

A: Use the vertical line test; if you can draw a vertical line anywhere that crosses more than one…

Q: Define a relation T from R to R as follows.for all real numbers X and Y, (X,Y)€T means that Y2-X2=1…

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Q: Find A and B so that the following function is continuous: + 3 x 2 f(x) = %3D a lax + b RIG

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Q: Differentiate the function.

A: Given f(u)=u1+lnu Now,differentiate function f(x) w.r.t to 'u'…

Q: 5. Assume that V × F = V × G. What is the most general relationship between F and G ?

A: ∇ x F = ∇x G =&gt; ∇ x (F - G) = 0

Q: Define the relation A,= [(x,x + 1): x E R] Show that A, is a function from R to R.

A: Given relation △x=x, x+1: x∈R is defined on Real number set R. Now a relation is said to be function…

Q: Consider the function f(x, y) = e-x²-y² defined on the rectangle -2<xs 2, -1 <y < 1.

A: In this question, we find the absolute maxima and minima by using suggested steps.

Q: Assume that f(x) and g(x) are both differentiable functions. Given f(3) = -2, -4, f'(3) = 8, and…

A: Given that f(x) and g(x) are both differentiable functions and  f3=-2, g3=-4, f'3=8, g'3=2

Q: Determine whether the function with u = x² – y² and v = is an analytic %3D x² + y² function or not.

A: The complex function, z(x,y)=u(x,y)+iv(x,y) is analytic in a domain D , if it satisfies the…

Q: Determine if the following functions are analytic or not: 1. f(z) = (z* + 1)³ – 3z* where z is the…

A: (i) The  given function is ;               fz = z*+13 - 3z* We know that a function  f is analytic…

Q: 19ver. Find y as a function of x if a?y" – 7xy' + 16y = 0, %3D y(1) = –5, y'(1) = –4. y =…

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Q: Let x, y € R. Then x^2+y^2 = 16 defines y as a function of x. True False

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Q: Determine whether the pairs of the functions are linearly inde- pendent or linearly dependent on the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Let f(x,y) = 2* + 6xy, find f(0, – 3), f(– 3,2), and f(3,2).

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Q: Let f : R → R be a function with the following property: f(x + y) = f(x) + f(y) for all x, Y E R.

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Q: Determine whether z is a function of x and y + z2 = 1

A: see below the answer and explanation

Q: Which of the following relations is a function? (Discuss your reas- JJ:N N (f = {(x, y) | x² + y² =…

A: Given are the relations f:ℕ→ℕf=(x,y)∣x2+y2=25 and   f:ℤ→ℤf=(x,y)∣x200=y200 A relation is called a…

Q: Define y as a function of x: 2xy + 5y2= 4   Don't forget the 5 in 5y^2

A: The given equation,     2xy+5y2=4

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

A: fx is differentiable and invertible function so that f(3)=4 and f'(3)=12

Q: Which of the following relations is not a function? Oy² = 1-2x² Oy+ 2 = 0 x² = 1-2y Oz=1

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Q: Use a formula to express y as a function of t if  y = 3x2 + 9x and x = t − 1.   y =

A: First of all, both equations i.e. y in terms of x and x in terms of t.

Q: Give an example of two functions f : R → R and g : R → R such that f is inj (go f) : R → R is not.

A: We have to given an example: According to definition:

Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Find f •g and gof ,where f (x) = x² + 1 and g(x) = x + 2, are functions from R to R.

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Q: If f(z) = u + iv is analytic function of z, show that a2 a2 2C. ây? 7 Ju? = p(p-1)uP-?|f'(2)}?

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Q: Find a function y(x) such that y'(x) = x² In(x³) – (x² + 1)¯ and y(1) = 2.

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Q: Differentiate implicitly the relation x³ + xy² = 2y³ – 4 to find y'. Then evaluate y'at (-1,–1)

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