A function f : D → R is called a Lipschitz function if there is a number K > 0 such that |f(x) – f(y)| < K|x – y| for all æ and y in the domain D. (a) Prove that a Lipschitz function satisfies the e-d criterion on its domain, and the conclude that it is uniformly continuous. (b) Let f(x) = Va for all r e [0, 1). Prove that f is uniformly continuous but is not a Lipschitz function.

Q: 1A-(구) -1 1 Then, ||A||1= 1 -2 Let A =

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Q: If A and B can be placed in a one-to-one correspondence, must A=B?

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A: LetWe have to evaluate the above integral.

Q: Lind Domin ond Ronge ? FlxJ=5+X り= メー9

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A: We use the properties of matrices to find the values of x and y.

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A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

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A: The dot product of two vectors is calculated as follows: a→·b→=xi^+yj^+zk^·ai^+bj^+ck^=ax+by+cz

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A: To prove AB = BA.

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A: Given, A=1232,  B=2-1-34

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A: Given, (12)(13)(14) and we have to write this in the form alpha(12), where a in A4. Similarly, write…

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A: Solution: Let x be the number of people in a household  y be the number of times they get sick in a…

Q: Let ā = (– 2, – 1, 3) and b = (- 5, 1, – 4). Find ā · b.

A: Given that , a→=-2 ,-1 ,3 and b→=-5 ,1 ,-4 a→·b→=?

Q: (1) and (.), (.) dz = Find the number of terms in where z = gu, v/ and u

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: ,3), calculate the value of a it the

A: We have to find the value .

Q: and y= If a = 3, then x =

A: Solve using the properties of trigonometric rations

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Q: Let D = {-2, -1, 0, 1}. Let E = {0, 1, 2, 3}.

A: Answer

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: Let u = (1, 2, –4), v = (-5, 3, -7), and w = (-1,4, 2). Perform the operation u. Type your answer...…

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Q: Let à =. Find |ā|.

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Q: Let à . Find al.

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Q: Find the adjoint of A (1 2 4 A =3 4 5 2 -2 2

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Q: Is x and y independent?

A: Given ,the joint probability density function (pdf) of (X,Y) isf(x,y)= Marginal pdf of X is =…

Q: State and Prove Pick’s Theorem.

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A: Given: ab=cd, b≠0, d≠0 For prove given expression, we do cross multiplication and simplify it as…

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A: We are using integration after decomposing it into partial fraction form

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A: Solution: The objective is to find the required values

Q: 12 13x5)

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Q: If a = (2, -1, 3) and b = (2, 2, 1), find the following. a x b = b x a =

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Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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Q: what would Z and MOE be ?

A: Here we have to identify the Critical value Z and and Margin of error MOE

Q: Do from b to e

A: Discrete probability distribution

Q: Let U = R, A =[-6, 3), B = (-1,5), and D = [-7, 1]. Find (i) AN Bº (ii) (BUD)e

A: We use De' Morgan's law and union, intersection and complement of set to answer the given question.

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.