thゃト IF Sequieree is divergent to prove THEN bounded below. it is

Q: if x 4.

A: The function gx is a piecewise defined function.

Q: Untersection of any point p is of р the Prove that two neigborhoods a neighborhood.

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Q: (b) En=1 m

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Q: What does it mean to say f : (a,b) →R is a bounded function? If a < b in R and f : (a,b) → R is…

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Q: Prove: If a &gt; 0, then (1/a) &gt; 0.

A: It is given that a&gt; 0.It is known that if ab &gt; 0 then a &gt; 0 or b &gt; 0 or a&lt; 0 or b…

Q: If there exists open ball B (a, r) such that B (a,r) nG = Ø then a is not limit point of G True…

A: TRUE

Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: A monotone sequence is convergent.

A: 1) If f is continuous on A then fn is also continuous  on A So The statement is true

Q: Use Greea's Theorem ond Compute the Counter clock wise cir culotivn of É around the closed urve C .…

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Q: t BLX,X) denoted set f al incod bounded operates an defined on ow hat fex every TE BLXX) for Hhe…

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Q: 7. has a fixed point. ) Prove that if f is a continuous function from [2, 5] to [2, 5], then f

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Q: (R,t) usuall top space and A=(0,1),B = (a,b); a<b. prove A=~B ??

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Q: f is Riemann integrable iff f is bounded and f has finite set of discontinuous points.

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Q: Show that in R with the usual topology, the only open sets connected by trajectories are the open…

A: Given that R with the usual topology  A collection of of subsets of R which can be expressed as a…

Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t&gt;0=0, t&lt;0 Therefore,…

Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: Find a and b such that 3 1 1 27 = a -3 + b -6 2 a = b =

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Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: chen T:lab]-→R is pschrA? on [aib] 7 there exist a consleant Cyo St Ifw-F(8)|< C1x-y1 for all xyE…

A: First we have to show that f is uniformly continuous on [a,b]

Q: Q3/ Let X = (0,1,2,...) and T = (0) U (Un.nE N), where Un = {n, n+1,n+ 2,...), show that whether…

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Q: let f [o2]→Rbe afunction if x<1 fex)= Is f Riemaninteglable? 下くx か

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Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: What is the Boundedness Theorem?

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Q: 4. Solve the equation z3 + 8i = 0

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Q: State true or false with brief justification   If T:X----->Y is continuous, linear and open, then…

A: Given statement is If T:X→Y is continuous, linear and open, then T is surjective.

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

Q: (b) Let # ACR be bounded below. Prove that Inf (A) =-Sup(-A). %3D

A: Let A is non-empty subset of real number . Let A be bounded below then we have to show that  Inf(A)…

Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

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Q: Poe thao exists u Gunjection x>X which i's not infection. X, X2, X2 De-fine : 9: 1→X n2,2. I (Xn) =…

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Q: Find the radus of ConvergeAce for

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Q: 1.49. (!) Let f and g be functions from R to R. For the sum and product of f and g (see Definition…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.