Consider a point s in R3. (a) Is Ne(s) bounded? Briefly explain. (b) Is N¿(s) open? Briefly explain. (c) Is Ne(s) strictly convex? Briefly explain.

Q: M=N

A: answer is in next step

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Q: 2. Below is the w is complete the

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Q: R Given: m ZRTS = 90; M MN is the 1 bisector of TS. Prove: TM is a median. T. N

A: In a triangle RTS , angle of RTS is 90 and MN↔ is perpendicular bisector of TS Midsegment Theorem:…

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A: Wr want to find the probability by chebycheves inequality.

Q: P Finel the funetiên whese first difference is e,

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Q: (d) Find the rank and nullity of A. rank(A) = nullity(A)

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A: Here we will use the concept of maxima and minima to solve this question

Q: 63. Given n nonzero numbers o1,...,on, show that the minimum value of S(x1....,xn) = xfo7 +..+ x…

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Q: Which inequality describes the restrictions on x according to the hinge theorem? 5x 95 5x + 3 3x+17…

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Q: Find and prove the minimum possible value of…

A: p + q + r + s >_ 4( pqrs )1/4 for all positive integers p, q, r and s.

Q: (c) Let z1 = 2+ 2i and let 22 =1+i. Prove that the triangle inequality |21 + z2| < |21| + |22|…

A: Left hand side is equal to, z1+z2=2+2i+1+i=3+3i=32+32=32 Right hand side is equal to,…

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A: For closed region , Sign of equality holds. Equation of sphere is -  x2+y2+z2=a2 ,where a is the…

Q: 62. Let D be the domain bounded by y = x2 +1 and y = 2. Prove the incquality 4 20 (x² dA 3

A: The domain is y=x2+1 and y=2. Sketch the domain D as shown below.

Q: b Let A be a continuous fuzzy quantity. If all the a-cuts of A are closed intervals then show that A…

A: In the question provided it is given that A is a continuous fuzzy quantity. The objective is to show…

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A: Disclaimer: Since, we are not providing any hand written solution currently, the answer has been…

Q: Culculate the iterated întegreat T/2

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Q: o Yes, zero is contained in the interval.

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Q: nd the supremum and infimum of the set D defined by D:= :neN

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Q: 8 If S has a maximum and a minimum then S is compact.

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Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

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Q: - Use the Exterior Angle Inequality to find an upper and lower bound for LMLK = y. %3D M 70° 50 K L.

A: Given: To Find: The upper and lower bound for ∠MLK=y° using exterior angle inequality

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A: size of the space streatched   by the set of n element is 2n+2

Q: A Moving to the next question prevents changes to this answer. Question 2 Let AcR be bounded and set…

A: Choose the correct

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A: we know domain of ln(x) is set all x for which x&gt;0.

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Q: 4- find the absolute max.and min. o f the function f = x² +y? Plate boun ded by = x +y? on the…

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Q: -[2.16] Let S be a nonempty set in R" and let x e S. Consider the set C = {y : y 2(х - х), A20, х E…

A: Given- Let S be a nonempty set in Rn and let x¯ ∈ S. Consider the set C = y : y = λx - x¯, λ ≥ 0, x…

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Q: The Canonical form of a hyperbolic PDE is F (ξ, η , u, ug , un ) %3D False True

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Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

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Q: Find the value of K that make s the funtion fcx) Continus : x*+ 3K メニ2; %3D 2K-X > 2

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Q: B. Use indirect proof 1. Show that: Vx€z, if x2- 6x+ 5 is even, then x is odd.

A: Given : x2-6x+5 is even for all x∈ℤ   To prove : x is odd As x2-6x+5 is even . So,  x2-6x+5=2m for…

Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: Part 1 of 5 - Part I Given the set X = {x € R³ : d(x,a) <r}, where d is the usual metric on R³. A…

A: A set is closed iff its complement is open. So a set is not open iff its complement is not closed.