5. Is there a number a such that Зx? + ах + а + 3 lim x→-2 x? + x – 2 | exists? If so, find the value of a and the value of the limit.

Q: Q1. By using the definition of the limit, discuss the limit of the function f:R - R if the value of…

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Q: 4] Compute the following limits, using the Algebraic Limit Theorem,where (x„) → 0. 1+2x, a) lim…

A: a) lim 1+2xn1+2xn-3x22 Since limit of xn is zero . Using lim cxn=climxn So, lim 2xn=2limxn=20=0…

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: Show that the limit does not exist: limit    (x^2+y-2)/(x-2y+4)                    (?,?)→(0,2) I…

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Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: Jse the two-path test to prove that the following limit does not exist. y* - 2x? lim 4 (x.y)-(0,0)…

A: Since tha value of both the limit is different  Hence the limit does not exist.

Q: Determine if the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R is uniform. If yes, is the limit…

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Q: Use l'Hôpital's rule to find the following limit. 3x-2x lim 3 X o 5x° +3

A: To use the L-Hospital rule to find  Lim(x tends to infinity) [3x³-2x]/[5x³+3]

Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: Use the definition of limits at infinity to prove the limit

A: Definition of limits helps to find the limit of the function. A value is said to be the limit of…

Q: and If lim f(x) = lim g(x) = +o and flx) =1 and gtxl = e, what is the limit of the division of !!…

A: As given limit is infinitely by infinity form so use L'hopital's rule and substitute the given…

Q: Evaluate the limit using L'Hospital's rule: e10x – 1– 10x - - lim x2

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Q: Q4 Evaluate the limit lim (x.y)-(0,0) 3x2+y xy cos y if it exist. If not, show that the limit does…

A: In this problem we compute the limit along x axis and along the line y=x .If these two limits are…

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: 2. Use L'Hospital's rule to evaluate the following limit. cosh(3x) – 1 lim x→0 x2

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Q: In finding the limit for  (x)2/x as x→+∞ by L'Hospital rule, which limit should appear in the late…

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Q: 3. Can f (x) approach a limit as x → c if f(c) is undefined? If so,

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Q: 2. Prove the following limit using the precise (that is, e- 8) definition of limit. lim (x + x) = 2…

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

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Q: 1 Q.3: Discuss the limit of f (x) : at x = 0", 0*,-∞,+∞, with graphs.

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Q: Evaluate the limit using L’Hôpital’s Rule

A: Given limit is: limx→∞x3+2x4-x We have to evaluate it by the method of L'Hospital's rule, So…

Q: If the limit lim (x,y)→(0,0) F(x, y) = 0 along the path of the form y = kx for any real number k…

A: Follow next step

Q: 2.a?y Using paths, show that the following limit does not exist. lim (x,y)→(0,0) 3x4 + y?

A: According to the given information, it is required to show that limit does not exist.

Q: Show that the following limit does not exist. ху lim (x. y)-(0, 0) 3x2 +2y2

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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: Find a value of the constant k such that the indicated limit exists. 8 -5 lim x-0 ekx +5

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Q: Use the definition of the limit ( epsolon - delta ) to show that lim of 1/z as z approaches -i

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Q: What must be multiplied to both numerator and denomination of lim→2 3-г-1 SO 2-x that the limit will…

A: We have to find multiplication factor for given Limit.

Q: When using the definition of limit to prove that L is the limit of f(x) as x approaches c, you find…

A: The ε-δ definition of a limit is an algebraically precise formulation of evaluating the limit of a…

Q: Use the e-8 definition of a limit at infinity to prove that lim = 0. %3D

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Q: Use l'Hospital's Rule to calculate the exact value of the limit ) as x→ 0- Az) fX) = e -1 and g(x) =…

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Q: x² - y? lim ) - (0, 0) х? + у? y

A: Here we have to show that, lim(x,y)→(0,0) x2-y2x2+y2

Q: lim x3 In(x) X→0+ to

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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: Show that the limit does not exist: (y² + x – 1)² - lim (x,y)→(1,0) (x – 1)2 + y4

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x.y)-(0,0) x²+y2

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Q: 2х — 5 lim 4x

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Q: 4. Use the e - 6 definition of limit to show that lim (2: +3i) = 2 + 5i. 2+1+1

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Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: 2. Use e -d of the limit to prove that lim z= 4

A: Given below the detailed solution

Q: 1. Show that the limit does not exist. xy? lim (x,y)→(0,0) x² + y4

A: This question is related to limit in two variables.

Q: Find the limit. lim (2 – x) tan(3«) %3D x>1

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Q: 4. Use the € & definition of limit to show that lim (2z+3i) = 2 + 5i. z+1+i

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

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Q: 5. Find the limit. lim (Inx)2

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Q: 8. Let f(x, y) be the function x3 + y3 xy? Show that the limit lim(9)→(0,0) f (x, y) does not exist…

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Q: Show that the following limit does not exist: (x – y²)2 lim (r,y) (0,0) ² + y4

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Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: Find the limit. lim Cn (3+x)- In (l+x)]

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