In a metric space (X,p), if lim un = u, lim v, = v, show that lim d(un, Vn) = d(u, v). %3! n-00

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Q: Does lim

A:

Q: (*+2x* -1) ? 5. What is f(-2) if lim, 5-3x 12 В. 6. C.- 15 D. -- А.

A: Given that: limx→-2x3+2x2-15-3x

Q: find its limit.

A:

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A: Solution  limx→∞Axn=0 , where A is constant and n>0

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Q: Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

A:

Q: Show the na

A: To prove that:                   ∫abF(x)dx=limn→∞ U(Pn,F)

Q: 47) lim √√3x-2 x-1 48) lim X->>0 x3 + 12x² - 5x 5x

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Q: Find the limit analytically

A: Given, limit function is

Q: find lim Cos(는)

A:

Q: 8. Evaluate the limit by using a change of variable. 1 X6 1 d. lim x→l_x³ Vx 2 x4 √x³ - 8 e. lim 1…

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Q: 山m x→イ cos'x COsx t G CCOSX t ? cos x x1

A:

Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: fnd 4. lim cosx)

A:

Q: Find lim x+x:

A:

Q: nd lim delta -> -4, tan(delta + 4) /5delta+20

A:

Q: Evaluate lim (3x . x+y) (х.у)-(4,5)

A:

Q: If the lim v 25- x2 exists.Find a . A) [-5,5) B) (-5,5] C) [-5,5] D) (-5,5)

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Q: Find limit x by drawing only

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Q: Illustrate how the product law, difference law, constant multiple law, and identity law are used to…

A: We Know that  Limit Laws : Let  and  be defined for all  over some open interval containing . Assume…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.