1 Find lim dt

Q: Prove that lim x->0 x4cos 2/x =0

A: Important: cos 2θ = 1 - 2sin2 θ

Q: prove that lim [x19 cos (1/x2)]=0 x->0

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Q: (2 -1) s lim z

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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: (1 cosr)dt 1. limx-0 2x -?

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Q: 1-coskx 2. lim kx = 0.

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Q: Prove that lim, Vn = 1.

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Q: xCosx-In(1+x)] х-Тапх, limx-ol limx-o[ a) х-Sinx c)

A: a ) given limit is as below:

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: Enter a whole or decimal number, or DNE for does not exist or undefined. lx-이 4 + | lim x →0-

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Q: 1) lim (1--)*

A: As per our guidelines we can solve only 1 question. The rest can be reposted.    In question  no 1…

Q: 2+ 1 ** Evaluate lim - X+ oL dt A B none of these 1- e? 1 4

A: Given that,  Now taking the integral term,

Q: Prove that lim x cos - = 7 %3D 1= 0.

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Q: Prove that lim x² cos(1/x²) = 0. x→0

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Q: 1. Evaluate: lim (lnr) h-0+

A: Given: limx→0+x3lnx As we know that; The Power law: ddxxn=nxn-1

Q: Show that lim→0 x2cos(1/x^2) = 0

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Q: 1 1 Use l'Hopital's rule to evaluate lim x→0+ In(1+x),

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Q: (금 1 Evaluate L = lim T→2 + x² – 5x + 6 -

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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: coshx Find lim. et

A: Coshx can be  written in terms of exponential as : Coshx = ex+e-x2

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

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Q: Find the limit.

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Q: Prove that lim (1/ nP) =0, p> 0.

A: Given the equation which to be prove

Q: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

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Q: ()- In(x) C. lim %3D

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Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: 4. Evaluate lim (cos x)¹/x². x-0

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Q: cosʻ(2x+3) lim

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Q: Find lim (e-2x cos x) (Hint: Squeeze Theor

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Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

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

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Q: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

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Q: Compute lim 0 tan-(5x) 5 25 undefined 1 25

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Q: 44

A: To prove,

Q: In x Apply L'Hop rule. lim

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

Q: 1. Find lim,→0 k e'

A:

Q: (1 1 Calculate lim X-+ x sinx

A: Find the limit

Q: 1 lim In csch (1– 2x,

A: Let L is the value of given Limit

Q: Find the limit.

A: Given,

Q: 2* – 1 x→0 V1 +x – 1 lim Evaluate

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Q: 2. Compute lim x" (1 + x)* – e). 1/x x→0

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Q: In (3t) lim t2

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

Q: Find the limit.

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Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…