Exercise 1. Let (X,dx) be a compact metric space. (a) Verify that dy(f, g) = E 2-"dx(f(n), g(n)) nƐN defines a metric on Y = {f : N → X}. (b) Show that Y is compact.

Q: M=N

A: answer is in next step

Q: Prove that  that the y=0 is the horiz.asymp.  and x=-1 and x=1 are vert.asymp, of y=coth-1x through…

A: As given that for the function y=coth-1x has verical asymptotes at x=-1 and x=1 and has horizontal…

Q: show that the rectaugle that has mancimum Qree for given PerimeTer is e sequare. in

A: Consider the provided question, We need to prove that the rectangle that has maximum area for a…

Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

A:

Q: Integrate the fallswingfuntinne aver the given regionr s R: the circle x+y=t and y=x? thiss

A:

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

A:

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: The radical center does not existif the circles are concentric TRUE FALSE

A:

Q: find fvelume of Solid f in the octant that is below porabalord そこ16-メ-9 planes X:0,9:0I and Z=0. and…

A:

Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Find two positive numbers whose product is 95 and whose sum is a minimum. The two numbers are (Type…

A:

Q: © Applyjing guaphicd amlyin to silve the fallomng graphical analyin to selve the n pieblen. muximiz…

A:

Q: What is the minimal perimeter that a rectangle can have if it has one ertex at the origin, one…

A: We have to find the value of the minimal perimeter of the given rectangle.

Q: Ray AB bisects CAT. If mLCAT= 30 and mL CAB= 2x + 10 then give the value of x.

A:

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

Q: Let -{) -() -E) --() by and 7 1 b2 ba Find conditions on bi, b2, by such that E span{at, a, .

A: NOTE: Refresh your page if you can't see any equations. . write all basis vectors in the matrix…

Q: The midpoint of v(2,10,14) is

A: Midpoint is found between 2 given coordinates.

Q: Find the image of the circle Iz| = 3 under the stereographic projection in the sphere.

A: We let G be a sphere in Euclidean three space. We want to obtain a picture of the sphere on a flat…

Q: 3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

A:

Q: Show that every point of R is zero distance from Q

A:

Q: Drive the frenet frame ,curvature and torsion of binomial indicatrix of hypocycloid

A: We need to Derive the frenet frame, curvature and torsion of binomial indicatrix of hypocycloid

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.