. What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

Q: Find o for e = 0.1 for the following limit. %3D lim 3x - 4 = 17

A: ε=0.1 and limx→7 3x-4=17

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: E valuate Dle followneg: lim メーフ+ 7x" – 4x? + 7x - 2 J +- 3 メ 3x° -8x"+ フメー458 -x一5 x3

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Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim I00…

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Q: 8. Use the alternate form of the denivative: lim f(x)-flc) to show that f(x) = | x + al %3D X→し is…

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Q: Evaluate the following limits: x? – 4 - lim x→-2 x2 + 9x + 14 x2 – 4 lim x→-0 x2 + 9x + 14 V3x2 – 72…

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Q: evaluate the limit. lim e2 'i+ In(t + 1)j + 4k

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Q: lim 4e-4x lim 5ex - 4 X-4 9x + 7x - 7 lim 2x2 - 2x X- +0

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Q: Find the limit. lim X-2 x+2 O 1/2 -00 O Does not exist

A: Answer is limit does not exist

Q: Estimate the limit numerically. lim e-13 x13 a. O b. 13 О с. O d. 0 O e. 1 8.

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Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

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Q: Find the limit. lim x-2/In x X x-0+ O -2 O e?

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Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: Find the limit (1+h)3 –1 lim h h→0

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Q: 1. Evaluate the following limit: x? -4 a. lim- 1+2x + 2x – 8 (x²-9) 2 b. lim 1+3 (x -3) (t - 3) c.…

A: If putting the value of variable value of function approaches 0/0 we should apply L hospital rule…

Q: IS In(x² – 1) 6. Evalaute lim x→0 cos(x) - 1

A: To find the limit of the function we have to find right as well as left limit of the function. First…

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

A:

Q: Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

A: We will use Chebychev's inequality to find the limit of given probability.

Q: Find the limit of the following: lim     e(2/3-x) x→3+

A: To evaluate the below right-hand limit

Q: 1. Use the e – d definition of the limit to show the following: - (a) lim(5x – 2) = 3 - (b) lim VI =…

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Q: In a lim T→0+ 2x

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Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

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Q: Calculate the following limits x2+4x-12 а) lim x-2 b) lim Vx +1 In(x+ 1) |x-21 X→ー1

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Q: Compute the following limits. -3x (c) lim In(r-9) - e (a) lim xoo e3x te-3x x+3+ (b) lim e4/(3-) T3-…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: Find the limit. 2 lim 1+ x4 О А. 2 О В. 0о O C. 0 O D. 1

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Q: Evaluate teh following fucntions

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

Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: b): Evaluate each of the following limits: 1- cos 3x 1)lim x→0 9x2

A: Given, limx→01-cos43x9x2

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: The value of k such that x2 lim kx + 7 x→1 x – 1 exists is

A: Given: The limit expression limx→1x2-kx+7x-1, To determine: The value of k such that the given limit…

Q: 2) Suppose that the limit of a function f(x) exists at z = a. If lim f(x) = M and lim f(x) = N, what…

A: Given:- f(x) exists at x=a We have to find the relation between M and N for given limit of a…

Q: Suppose that f(x) = 2cos (n/3 x) and the graph of g(x) is given by: y = g(x) 2 1 -5 -4 i ż 3 4 5 x…

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Q: 1. Show that for all f e L'(R) lim

A: To show: limδ→1∫f(x)-fxδdx=0 Concept used: ∫fxdx=Fx+c Chain rule: ∫fxadx=1aFx+c

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: b): Evaluate each of the following limits: 1- cos* 3x 1)lim x→0 9x2

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Q: Evaluate the given limits: a) 2x3 + 5x² + x – 1 lim x→+0 e2x -

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

A: Given, limx→1-1-x=0

Q: Is In(x² – 1) - 1) 6. Evalaute lim n cos(x)-1 r lulx2-1) lem lulx²-1)

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Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: By definition of limit , find o from the following * lim (-3x – 2) =1 e = 0.03 x→-1

A: Since you have asked multiple questions, we will solve first question for you. If you want other…

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: Determine the following limits at infinity. f1x2 xSo g1x2 lim if f1x2 S 100,000 and g1x2 S 00 as x S…

A: Given information: The function f(x) approaches 100,000 and g(x) approaches infinity as x approaches…

Q: Q1: Find the limit of the following х-2 2x2+1 tan nx 1) lim- 2) lim x-0 (2-x)(2+x) 3) lim x-2 x²-4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the relationship between e and s needed to prove S=

A:

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: a) Show that for any & > 0 and S₂ = ₁X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n n→∞

A: We will use Chebychev's inequality to find the limit of the given probability.

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…