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

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: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

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Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

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Q: 11. lim x→-4 х2—16 2x2+9x+4 z2-36 12. lim マー6 z-6

A: We have to find the above limit. Then we get,…

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

A: topic - limits

Q: Find the limit infimum and limit supremum of the following x₂ = Yn where Yn is bounded. Хр n lim…

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Q: 2) Use the e-8 method to prove lim (3x - 1) = 2 Given e > 0, there exists a d such that if 0 < |z-a…

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Q: Find the limit. /h² + 10h + 11 - /11 lim h→0* h² + 10h + 11 - /11 lim h h→0*

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Q: 3. Show that the largest value of o that can be used for some e > 0 if lim (2+ 5x) = 17 is エ→3 anx"…

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Q: Find the value of a, b, andc such that the limit a + bx + cx - cos(2x) lim x4 exists. a = (Enter…

A: →When limit is of the form 00 or ∞∞ then L'Hospital rule is used.     In this rule, take the…

Q: Find the limit. 시h2 + 10h+ 19-119 lim h vh? + 10h + 19 - /19 lim h h→0* II

A: Given: Limit equation is given.

Q: II. Apply the limit laws on the following: lim x→2 `x3-x 1. 2. lim (Vx/V) X-1 .cos x lim (*)(**+x²…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

Q: Suppose the inequality (x² – 4x + 3) < f (x) < cos ( TX *) holds for all values of x. 2 Find lim f(…

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Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

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Q: The value of the constant k such that .2 k x +7 lim exits is X - 1 X → 1 7 - 7 -8 -6

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Q: (1) Evaluate the limit, if it exists. (a) x² + x - 2 lim t→1 x² - 4.x + 3 (b) x - 81 lim x→81 Vx - 9

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Q: Evaluate the following limits analytically, if it exists. (a) Vx+14 – 1 lim x→-10 2x (b) 5x +7x lim…

A: Given problem:-

Q: ΜΑΤΗ-101A 7. Find the limit. lim ( x2 cos x→0

A: We have to solve the given expression   limx→0x2cos1x

Q: Find all values of c such that the limit exists.

A: Solution:Given         limx→∞x2-5x-6x-cTo find all values of c such that the limit exists.

Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

Q: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

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: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

Q: 23: Eva In x² x-1x²-9 Evaluate these limits: 1) lim.

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Q: 1. Show that for all f e L'(R) lim %3D

A: Put the delta = 1 in integral function

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: In(x)-In(a) 14. lim %3D Xa X-a (A) = (B) In(x)NT 92 anevni art

A: Given, limx→ alnx-lnax-a

Q: Find all values of c such that the limit exists.

A: Given: limx→cx2-5x-6x-c for finding value of c for given limit to exists, we factorize numerator of…

Q: (1) Evaluate the indicated limits, if exist (x³ + 1) -x (а) lim r+0 V9 + x² (b) lim In I→1+ (c) lim…

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Q: 11. Determine the limits. In(x) a. lim X→1 X-1

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Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

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Q: Prove lim(Vn+1- n)=c 8. 0 =

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Q: find the valve (s) of K . such that lim Oxists X-D-2 affx) erists KK - 3 メ5-2 2. K 7-2

A: topic - limits

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

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Q: Find the lim inf (xn) and lim sup (xn) of Xn = √1 + n² 2n - 5

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Q: e -e lim is z0 In(1+ 2x)

A: Given limit:

Q: Find the limit. Iim (e 4/x x-0 9x) x/2

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Q: Determine the value for c so that lim f(x) exists. X→3 1 f(x) = 3*+c, for x3

A: Given that,

Q: Find the lim inf (xn) and lim sup (x₂) of Xn = COS nπ

A: I have calculated the limits

Q: Evaluate the limit t3 – t lim t→1 t2 – 1

A: We have to find the given limit.

Q: Evaluate the limit given below. lim 9ti+ 1²-16 1²-4t j+ k 2 (→ 4

A:

Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

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

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Q: 8. Find the following limits: Vx+6-3 lim 91 x-6x? lim а) b) X-3 7+3x x+3

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Q: In(x), 5 s x s 16 f(x) A = lim n- o 2 i = 1

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Q: 1.1. Find the limit or show that it does not exist. (a) lim (e + 2 cos 3x) (b) lim vx + ax - x2 + Bx…

A: Note:- In given problem, first problem already has two sub-parts. So, according to guidelines, we…

Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

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Q: The value of the constant k such that x²– kx+6 lim exits is X→1 х—1 б -6 -7 7 -8 8.

A: 1). From the given problem:   fx=2x+14   From the power law:   dxndx=nxn-1.   So,…

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.