Suppose that {n} is a sequence of real numbers satisfying lim xn = 1. Use n→∞ in the text book to prove that lim (1+2xn) = 3.

Q: L3x* -3x +b for all X, If bx < alx) evaluate lim 96x)

A: Concept:

Q: 2 Compute limx→16; 1-x2 1 X-1

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Q: In (x+1) lim log, x f)

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Q: Show that lim [((-1)^n ∙ n)/(n^2 + 1)] = 0

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Q: Q4\ find limit of the following x² - 2 1- lim Vx-2 X2

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Q: Let fn(x) = nve-na. For a fixed real number x (for example in the interval [0, 1]) this is simply a…

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Q: Find the limits in Exercise

A: Given: Let y=limt→6 8t-5t-7  To Find: To evaluate the given limit.

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

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Q: VE-5 (c) lim I-25 - 25 T

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Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: Show that lim e/n = 1 for any constant c> 1. Use the squeeze theorem (or any other method) to…

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Q: x -1- V3x +1 V3x + 1 lim x-5 x - 5

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Q: (d) lim 1-0 1 +3 - 3/1 I

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Q: う lim -3K -×)。 X 00

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Q: x-2 lim Jx-2

A: Find the limit limx→2x2-2x-2.

Q: Calculate the limit

A: We have to evaluate the following limit: limx→∞9x3+x-x32

Q: 3* –1 lim V1+x -1,

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Q: 4x2+11х-3 (i) lim x→-3 9—х2 (ii) lim 2 -1 *-4 х36 6-х Vx2+9-V2x2+9 (iii) lim х-0 VЗx2+4-V2х2+4

A: We will solve the following

Q: correspondig limit x' +x -8x-12 a) lím x* +4x' +5x + 4x +4

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Q: Let g(t) : 3 - VE t – 9 - Find the value of lim_9 g(t), or state that it does not exist.

A: g(t)=3-tt-9

Q: Find the limit of lim x(√64x²5 ∞0++* √64x²14) = = lim x(√64x²5 -5-√√64x²-14) ∞0++x

A: limx→∞x64x2-5-64x2-14

Q: 7) Show that lim = 1. 200 (z-i)3

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Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: In (1+x) lim

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Q: 1 lim t→0+ (뉴 1 Vt2 +t,

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Q: In x Apply L'Hop rule. lim

A: We have to find the limit by using Lhospital rule.

Q: 1 x-1 x-1 ln x 3) lim

A: Explanation of the answer is as follows