s Show that in the metric space (R, 1.1), Q = 4, (Q')"=$ Cinterior of rational numbers and interior of irmational S. %3D numbers' are empty set)

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Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

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Q: sent that by a positiv ntity N(0) is 2.

A: Given as, dNdt=?N0=?

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Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

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Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

Q: wherer € [1, 5]. Use 5 nodes to u intervals. 1. Use Trapezoid rule to approxim

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Q: If ø + SCR is bounded above, then .S has a supremum إختر واحداً: ibs

A: I have proved by contradiction

Q: let M= To,2] anel d be bhe usual metric then d is not compact or Compact ?

A: A set is said to be compact if and only if it is closed and bounded.

Q: Q2. In the circle Izl = 1, Find the upper bound for 1924+327+2

A: pleas see the next step for solution

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Q: O Find Valume bounded by %3D

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Q: Find the deriratire of y tanx usim the Difinition Rule

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Q: If X = {a, b} , how many metric can be de fined on X %3D infinite O none O only one O only finite

A: only one

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Q: Find 2 pOsitive real numbers x and y such that their s um is 40 and their product is as large as…

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Q: graph'the Sorution to the follow imy inginequratityon animber line nur (x-2) (x+5) z O

A: Solving the problem by doing the graph.

Q: Let V and W be finite - dimensionl vecter s pace over

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Q: Prove by sequences that the open balls in R^n with the usual (Euclidean) metric are not compact

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Q: Since, F is bounded both in LOR) and in lIR), it is Latnded in LLIR) forall fe[1,0) (Prdtem 31).

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Q: 7. Assume that f:XY is a function from one metric space (X,d,) to another(Y,d,). Prove that f is…

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Q: If o + SCR is bounded above, then S has a supremum. Select one: True False

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A: To solve the improper integral

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Q: If ffinite or in finite) Contable set, thers prave that At CS}=0

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