2. Evaluate the following: Va2-x² So Sa* x² ydydx а. xsin x b. lim-2cos x+e

Q: 42. Prove that if lim "O = 5, then lim h(t) = 15.

A: It is given that To prove that

Q: Compute the indicated limits. 5x + 5 lim cos 2x2 – 3x – 5 ||

A: topic - limits

Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Compute each of the following limits. (a) (i) lim 7x²5 x→-1 x²-25 (ii) lim X-5 x+5 (iii) lim x+2 x-2…

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Q: Compute the following limits exactly. Vx+22 -10 lim X 78 X-78

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Q: Compute the following limits. 4-(2+h) (a) lim (b) lim - x-2 h→0

A: Using rules of limits.

Q: can this be evalnated by using L'HOSpital's Ruie? lim Trxln(x) Itxen(x) (メ-)nx

A: The given limit can we evaluated by using algebra of limits.

Q: Pick 8 of 10: Prove or provide a counterexample. lim Sn =0 if and only if lim s,=0

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Q: 2.14 Show anx" + ... a12 + ao lim n an bn .. provided that b, # 0.

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Q: (1) Evaluate the following x²+3x (a) lim x-0 бх-18 x²-5x (b) lim x-3 x-3 x²+5x+4 (c) lim x-0 (d) lim…

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Q: S* 56sin(t")dt Evaluate the limit lim .8

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Q: find the Value of the limil [z(そ-e 241 lim

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Q: 1. a. Evaluate the following limit: 2x3-128. lim(**-1: X→4 Vx-2

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Q: Evaluate the following: 1. lim (et+t)¹/t t→0+ z4-z²-2z+2 2. lim z 1 z8-2z4+1

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Q: Show that if xn ≤ yn ≤ zn for all n ∈ N, and if lim xn = lim zn = l, then lim yn = l as well.

A: Given xn≤yn≤zn And also given lim xn=lim zn=l

Q: in SinSX 3K lim 2sin SX lia o X--0 evaluate the limit =?

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Q: 1 Ask for the answer to limx(1– e* ).

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Q: in Q5. Find the value of the limit: lim in — е 2 2+1 Z→e 2

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Q: 3. lim (4x+1) wt x

A: Given that;  Lim x-0+  (4x+1)^cotx

Q: If A = lim ("C " C " C_ " C ……." C )m(a+1) then A² is equal to

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Q: 3x - 3-* 3) lim x00 3x + 3-x

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Q: a In x (b) lim 100 I+ In x

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Q: 1. Use the definition to establish each of the followii (a) limx→2(2x– 7) = –3 (b) lim→1 T = (c)…

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Q: min 1) In formally proving that lim (x + x) 42, let e > 0 be arbitrary. Choose & %3D Determine m. m…

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Q: Find the following limit. lim (5x)6x X+0+ lim (5x)ôx | (Type an exact answer.) l X-0+

A: Given:

Q: Evaluate the following limits: 14и+1-3 a. lim u→2 и — 2 e4x -1-4x b. lim x -4x + 2x – 7 c. lim 8х*…

A: We are solving (a) question for you. If you want solution of some other question than please mention…

Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: Find a S that works for E=0. for the following limit lim -5x-7=-187 X76

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Q: 15. Find the following limit V2x+5–1 lim x→-2 x+2

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Q: In(9x) (d) lim x2

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Q: lim el -1 dt 61-12-e

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Q: 2) let fcx)=メメ6, tind a) limfix) X-72 bllim fex? メー70 c) lim fox) メーラ3

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Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

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Q: 1. Use L'Hospital's Rule to compute In(1+x) – lim | x2 2 Compute

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Q: Show that In x = 1. T bae amdinegoltox-1xlq ordt lim

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Q: Evaluate the following limits 2x2 – 3x + 2 1) lim x-3 2x3 - 3x + 1 z2 – 25 2) lim z--5 z+5 x² – 3x –…

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Q: 3. Find the following limits: x2 +5x +6 (a) lim x-3 x2 + 4x + 3 Vx2 + 5x +7 (b) lim 5 – 2x (c) lim…

A: As per our guidelines, we can not solve  more than 3 subparts so please repost  the remaining  part…

Q: Find the limit, if it exists. If it doe 3a + 3x + 4 lim 202 + Enter your an Enter DNE fo

A: We have to find  the limit .

Q: Evaluate the following limits.

A: Consider the given limit  limx→1∫1x2et3dtx-1

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

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Q: Compute the following limits exactly. 5* -7x +11 (a) lim x3+3x-4 X2 X TIX (b) lim 13sin(-A)-/24x +17…

A: Consider the limits a)limx→25x−7x+11x3+3x−4b)limx→613sinπx4−24x+17

Q: Exercise 2. Find the following limits 3x +1 1-3x² 3x +1 1) lim to 2x + 5 2) lim X+ 2x +5 3) lim x-…

A: Use limit concept

Q: 1. Find lim,→0 k e'

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Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Evaluate lim,0+ e(1/z) .

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Q: Evaluate the following limits: 5x +3 lim lim 3h –5 e h→0 a b x→3 x-1 lim 3x(x+4) x2 2h – h? lim d h

A: In the given question we have to find the given limits.

Q: In (3t) lim t2

A: Given : f(t) = ln(3t)/t² To find : Limit of the function

Q: Evaluate the following limits. 2. e* + e-*-2 a) lim b) lim (1 +2x) 3/ 3/x x2 c) lim x2 In x x-0*

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 1+2- 12 - 4x + 4

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.