show that : Limx→0    1/ (x – 1) + 1/( x + 1)  ) /x = −2

Q: Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?

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Q: Find the limit, if it exists.

A: Here given as

Q: 2 4. lim x-3+ \3-x 4 9-x2,

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Q: Estimate the limit numerically. ++7,000x³+ 800,000 lim 2x° + 1,269x³ 8. O to∞ 2.

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Q: Find the constant a such that Va ax +4-2 lim

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Q: Use l’Hospital’s rule where applicable to find the limit.

A: the given limit is: limx→08x6+3x4-9x9x7-2x4+x3 we have to evaluate the given limit.

Q: Use the Squeeze Theorem to prove lim,e-*arctan(x) = 0.

A: limx→∞e-xarctanx=0 Now, -π2<arctanx<π2                       ∵Range of arctanx is -π2,…

Q: lim x² ln x x-0*

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Q: (b) Show that if lim sn = +o∞ and lim tm > -x, then lim($n + tn) = +0.

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Q: Calculate the limit limx→13√x−1x−1.

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Q: Calculate the limit lim 2 / 5x-15 as x goes to 3^+

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Q: Use definiction to १r० v of Conkegene to lim n+4

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Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: In (1 +) lim t1/2

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Q: a) lim 2x e* +In x = ?

A: To find: The value of limit limx→+∞e3x+ln xe2x+x2. Concept used: Properties of limit:…

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: - Show that lim sin a =D0.

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

Q: Evaluate the limit: sin(5x) cos(6x). lim x→0

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Q: Compute the indicated limit. 5x2 – 5x – 3 lim x00 4x – 2x? – 7

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Q: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: lim(4x – 3) = 9 x→3

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Q: Find the value of the limit: 3 tan(4x)– 12x lim

A: From the given problem:   limx→03tan4x-12xx3   This problem can be solved by the series expansion of…

Q: Estimate the limit numerically. x+14x + 49 lim x+7

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Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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Q: Show that lim sin( does x→0 x2 .not exist

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Q: Find the limit. lim tan5x In2x = x→0+ %3D

A: Given :   limx→0+ tan5xln2x

Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: Use Squeeze Theorem to evaluate -2x lim e COS x x 00

A: Based on the squeeze theorem or it is also been called sandwich theorem we can evaluate the limit by…

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: Find the limit: limx 1(x2 + x + 2)/( x + 1)

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Q: Evaluate the limit: cos²(x) – cos(2x) lim

A: We have to find the limit

Q: Use continuity to evaluate the limit. 16 + Vx lim 16 + x

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Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

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Q: Compute this limit to infinity   limx→∞ of (7x^3 + 2020x+ 4)/(πx^3+ 18x^2+ 12)

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Q: Show that lim- e +1 does not exist. 1/x

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Q: Find the limit. limx 0 √(x2 + 4)

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Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: 1 Find lim dt

A: The given data is: limx→∞1x∫1xdtt  To find the value of the limit.

Q: lim(4x – 3) = 5 x→2

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Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

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Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

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Q: Use continuity to evaluate the limit. 8 + Vx lim 8 + x

A: We have to evaluate limx→18+x8+x Important formula  If fx is continuous function then limx→afx=fa

Q: Evaluate the limit. x2 – 2x + sinr lim

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Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

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Q: Find the limit: limx→0​ x3sin(1/3x​3)

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Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: Find the limit. lim etan x x-(9x/2)+

A: We have to find the given limit

Q: calculate the limit.

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.