Show if the following limit is indeterminate. If yes, evaluate using C'Hopital's Rule. а а (x²–1) – (x7 + 1) lim b - · , where a and b are nonzero constants b x→1 (xZ-1) – (x2 + 1)

Q: Let f(x) =, where Lx] is the greatest integer function. Show that for x + 0, 69. Then use the…

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Q: 4 Find the limit: lim t+0 t 4 et – 1, (Enter undefined if the limit does not exist.)

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

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Q: Show that the limit does not exist. (x + y)² lim (7,y)→(0,0) x² + y²

A: We have to check

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: C. Prove that the limit does not exist. 1. lim (xy)-(0,0) x*+3y

A: We need to prove that limit does not exist.Below find the details solution in image.

Q: Show that the following limit ry lim (.v)-(0,0) 22 +y? does not exist.

A: Substitute y=mx, and check by applying limit.

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: a. Evaluate the following limit using L'Hopital's Rule. Rx2-5 lim x→∞ e2Rx 1-е-Rx + lim e 3x

A: In the given problem consider the first term.

Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

Q: show that L’Hôpital’s Rule is applicable to the limit as x →±∞and evaluate.

A: Given,

Q: Use the Two-Path test to show that the following limit does not exist. (Use y=x2) lim (x,y)→(0,0)…

A: Using Two-Path test we will evaluate.

Q: 2. Use the definition of the appropriate limit to show (a) limr→∞(2x² + 4x – 1)/(3r³ + 1) 0. - (b)…

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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: Evaluate the following limits (if exist): 1-cos(ax) (c) lim- a+0 (d) lim/Vxr'+x-Vx°-cx), where c is…

A: To evaluate the given limit we are using L- Hospital rule

Q: Use l'Hôpital's Rule to evaluate the limit. cos (3x)-1 lim x² 2.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

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. Evaluate the following limit using L'Hopital's Rule. Rx²-5 lim e2Rx 1-e¬Rx + lim e3x

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Q: 3, Use the definition of limit (E & 8) to show that lim (2.x+iy)-4i, where z=x+ iy. 21

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Q: Show that the limit does not exist. (x + y)² lim (1,y)→(0,0) x² + y²

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Q: If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what…

A: Summarizing the given information:             . We need to find out that at what points c, we…

Q: 1. Evaluate the following limits (DO NOT use L'Hopital's Rule): V7+ 2x - 3 (a) lim 1-r 42021 +3 (b)…

A: 1. (a) limx→1 7+2x-31-x

Q: Use the e – 8 definition of the limit to prove that lim x2 – 2 = 2. %3D - x→2

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Q: Use the Squeeze Theorem to evaluate the limit lim f(x), if 2x 1< f(r) < 2 on [-1, 3].

A: Squeeeze Theorem: Suppose that g(x)≤f(x)≤h(x) for all x close to a but not equal to a. If…

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

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Q: Find limit, or show that it does not exist. 2x²y (x,y)¬(0,0) x*+y2 lim

A: Consider the given: limx, y→0, 02x2yx4+y2Find two different paths to approach the point that gives…

Q: Prove the following limit, where the Squeeze Theorem is used: lim, 0(xtan-1(x)) = 0

A: Let us try to understand concept of Squeeze theorem-

Q: 3x²+2x- 3 3. prove that with the help of the limit definition (with necessary analy si)

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Q: Use the Squeeze Theorem to find the following limit when c = 0, 2 – x² s f(x) < 2 + x². lim f(x)

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Q: Use the two-path test to prove that the following limit does not exist. y-2x2 lim y+x (x.y)-(0,0)

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Q: 8. Use L'Hopital rule to determine whether the limit exists, and evaluate it if it does. 1 - t lim…

A: Given,          limt→0et-1-tt2

Q: (a) Calculate the limit lim (z,y)→(0,0) x³ + y*' or show that it does not exist.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Show if the following limit is indeterminate. If yes, evaluate using L'Hopital's Rule. а а (xZ-1)…

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Q: 1. Show that the limit lim (2,y)(0,0) In(1 – a2)+ y* x² + y4 does not exist.

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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: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: 1. Prove that lim (10r – 7) = 3 using epsilon-delta definition of a limit.

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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: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

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

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Q: a. Evaluate the following limit using L'Hopital's Rule. Rx2-5 lim x→0 e2Rx 1-e-Rx + lim- e 3x x→0…

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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: Use the definition of "limit of f at c" to prove the limit of lim, 3(x² – 5x + 1) = -5

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Q: yA - 2x? lim 4 - 2х 2 (х., у)- (0,0) у +х 4

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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: Show that the_limit exists : 2x²siny 2), lim (x,y)→(0,0) 2x² + y²

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