Evaluate: lim ||r||; where ||r|| is the greatest integer less than r. I3- 3. 2.99999 Limit Does Not Exist

Q: Suppose lim, An = 1. Prove that 1 lim E(-1)*a2k = 0. n-00 n k=1

A: Given that limn→∞an=1. To prove limn→∞1n∑k=1n-1ka2k=0.

Q: Suppose that c is a real number and that lim f(x) and lim g(x) both exist. Give the 12 limit…

A: Use the given limit conditions and write the theorems. 1…

Q: Q. 3: Show that limit Lim does not exist

A: We just require simple knowlegde of limits problem

Q: 3 Find the limit: lim t 3 et – 1 - (Enter undefined if the limit does not exist.)

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Q: Q: Prove that Lim %3D n-a

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Q: V2x-V6-x 23.. lim X-2 4-x2

A: Given, limx→22x-6-x4-x2

Q: (1) The parts in this question are not related to each other. 4 (a) Using thee – ddefinition of…

A: Definition of limit: To each ε>0, there exist a positive number δ>0 such that, when…

Q: Use the E-8 definition of limit to prove that lim x2= 16.

A: The ε-δ definition of limit, limx→4x2=16

Q: Find the limit, if it exists. x2 - 36 lim X6 X-6 O12 ) 1 Does not exist 6. OOOO

A:

Q: Let n be a positive integer. For which n are the two infinite one- sided limits lim 1/x" equal?

A: Let n be a positive integer. for which n are the two infinite one sided limits limx→0±1xn equal. for…

Q: Use the limit definition to prove that lim n→∞ n-2 = 0.

A: n→∞ n-2 = 0

Q: 1.) Calculate the limit: lim(2x² – 6x +1)

A: We have to find the limit of the function: limx→22x2-6x+1 Since this is determinate limit so we just…

Q: Using the precise definition of a limit, à in terms of & for lim (2-3x) = -4 is E/-3 X-2 A) True B…

A:

Q: - What is the limit of lim 5*? X--00 A. -00 В. О С. 1 D. +00

A: limx→2 x3+13=23+13=93=33=1

Q: Prove, using the e-8 definition of limit, that: (a) (b) lim ²+1=2 24-1

A:

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: Prove that lim (2a2 + 3r + 6) = 5 using the e, 8 definition of a limit. %3D a -1

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Q: Evaluate the limit. lim x² In x x→0+

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Q: 3. Prove lim(a – 5x + 6) O using the epsilon-delta definition of a limit.

A: Explanation of the answer is as follows

Q: Use the e-N definition of limits to show that 2n -15 lim = 1. %3D n0o 2n - 13

A: The objective to show that limn→∞2n-152n-13=1.

Q: Evaluate the limit. lim 2h+3 h245h+2

A: Topic - limits. The given limit is limh→−1 2h2+3h2+5h+2.

Q: Use an appropriate definition to prove the following limits. g³ – 16x4 = 1 x + 2 9x² + 4 (а) lim…

A: We prove the given limits: limx→5+x+2x2-25=∞ limx→∞x5-16x4x5+4x2=1 limx→-∞9x2+4x+2=-3

Q: Use the Basic Limit Laws to evaluate:

A:

Q: Exercise 1: Provide an e-6 proof for the following limits (a) lim 33x21 r+3 (b) lim 2-1|

A: To establish the limits of the function using epsilon -delta definition

Q: 1. Find the following limit, if it exists, or show that limit does not exist lim

A: Here we have to find the limit. lim(x,y)→(0,0)x2-xy+y2x2+y2

Q: 1. (a) Use the e - 8 definition of a limit to prove lim(7x + 3) = 38. X5 t010-1123.then fex)-LI…

A: Given,

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: 4. Evaluate the following limit or show that it does not exist. 1 lim 2 u +u,

A: To evaluate the limit,  limu→01u-1u2+u

Q: Using the e - N definition of a limit, prove that 8n lim n+00 4 = 2 4n – 1 -

A:

Q: Compute the limit: lim (1+3x)^(-5/x) x→0

A: We have to evaluate the given limit.

Q: 10. Prove that lim x2 = 4 using the epsilon-delta definition of a limit. %3D X-2

A: limx→2x2=4

Q: Evaluate the limit. lim 3 x-1 O-1 O1 O3 Does not exist

A:

Q: 8 Evaluate the limit lim [(z-1)(3- 2i)+1-31] and use the definition of the limit (e-8) z+2+i to…

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Q: Prove the following using the definition of a limit. n - 1 (a) lim 1 n+on+ 1 (b) lim (2x² − 3) = −3…

A: Given a) limn→∞n-1n+1=1b)limx→0(2x2-3)=-3c) limx→2-1x2-4=+∞

Q: Prove that lim r = 2 using the e-8-definition. Hint: VI - 2 = VT + 2

A:

Q: Q1. Compute the following limits if it exists. √x+2-3. 1-lim( x-7 2-lim (7x²+x+1) x→∞0 4x²+3x

A:

Q: 3 Evaluate the limit lim [(2-1)(3– 2i)+1–3i] and use the definition of the limit (e-6) z-2+i to…

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Q: With regard to the limit lim x² = 25, Find a 8 such that |x² – 25| < 10¬3 if 0 < |x – 5| < 8.

A: We are given limx--&gt;5  X^2 = 25 We have to find delta , and we can find it by applying definition…

Q: 1 Use the definition of the limit (ɛ – 8) to show that 1 lim = i. z-i z

A: We will prove the given limit.

Q: Evaluate the limit 33 – - lim s-1 s2 – 1

A:

Q: x2-4x+3 21. lim X-1 x2-1

A: =?

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: To Prove - limx→3 x2-7x+12x-3 = -1Cosidering LHS - limx→3 x2-7x+12x-3 = limx→3 x2-3xx-4x+12x-3limx→3…

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

A:

Q: Evaluate Hhe following Limit lim 43+2)2-9n-18 n3-9K

A:

Q: 4. Use the definition of a limit to prove that lim z = a* for any real number a.

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Q: Can anyone solve this question please ? Many Thanks

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Q: 2. Compute each limit below using limit laws. 7+3x (a) lim 7+3x (b) lim r-4 4-x 7+3x 4-X

A: we have to find the following limit

Q: # 11. The lim,→-4 x²+ cx+c+5 x² + 5x+4 exists. What is the value of “c“? What is the value of the…

A: