2 -z+1-i Prove that lim =1- :l+i z- 2z+2 2

Q: 3- Vx Determine lim- x+4 x-9

A: Given limx→43-xx-9

Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

A:

Q: f has domain of (-∞,–1)U(-1,2)U(2,00) lim f(x)=- %3D x→ -1" lim f(x)=- x→ -1* lim f(x)=3 x→2

A:

Q: lim a'/z 2-

A: Given:

Q: (2 -1) s lim z

A:

Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

A:

Q: 2. Prove that a. lim, b. lim,1

A:

Q: Prove, using the formal definition, that limx→ 8 [(x)^1/3 = 2.]

A: The definition of limit is  limn→∞an=l foe each ε>0, there is a positive integer N such that…

Q: Show that limxy)H(-2,0) g(x, y) does not exist given that (x + 2)³y? (x + 2)6 + 3y4' 0, if (x, y) #…

A:

Q: Determine the limit: lim 1+n-'sin3(n) А. С. -1 1, B.

A: Introduction: When we deal with sine or cosine function in limits, we follow the inequality sinx≤1.…

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Prove limx→∞(1/x)=0

A:

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: lim- LIMIT VALUE: z²-16

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

Q: Find the limit.

A:

Q: Using e – N description to prove that lim - = 0.

A:

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: -4 Determine the limit: lim -i (и — 1)2

A:

Q: 6-2x Prove by definition that lim 4. 3

A:

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

A:

Q: 40. Prove that lim Vx esin(7/x) = 0. 41-46 Find the limit, if it exists. If the lim explain why.

A:

Q: 1. Find the limits. (Don't use L'hopital Rule) V2h+1-1 a. lim h-0 b. lim_(x – 3) -2| x--2 (x-2)

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: Prove the limit doesn't exist

A: cc

Q: Find the value of a such that exists and find the limit. limx-> -1 (2x2-ax-14)/(x2 -2x-3)

A: Given, limx→-1(2x2-ax-14)(x2 -2x-3)

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

A: our objective is to find the limit

Q: lim -3- tan-() = lim-otan-ly %3D True False

A:

Q: 1:3.5. - - (2n-1) now lim lim (n+1)! 1.3. 5-- - (2n-1)

A: Step1: Here to calculate the limit we value we have used the limit ratio test , where we the given…

Q: Prove that lim5 (x2) = 25

A:

Q: Prove lim 7-x =6 using the ɛ,8 definition (precise definition) of a limit. x2 2

A: Given data:     The given expression for the limit of the function is: .   The given expression for…

Q: EXAMPLES. Observe that iz +3 lim z→-1 z +1 z +1 =D0 since lim %3D z→-1 iz + 3

A: Now, limz→-1z+1iz+3=-1+1i(1)+3                 =0-1+3                 =0…

Q: 6n + 2 3. n→∞ 2n + 1 3. Using the definition (i.e. N, E), prove that lim

A:

Q: 7) Show that lim = 1. 200 (z-i)3

A:

Q: Compute the exist i. lim 8+iz 2--2i z+4 following limies if they . ¡i. Gm Rez.

A:

Q: lim cos nл| 2n-1 - 2n+2

A: Use : cos x =1-x22!+x44! + ...........

Q: 18 -a+1 Find the limit lim a9 2x2+3x-1

A: Given, limx→918x2-x+12x2+3x-1   To evaluate limit

Q: 4. Determine the infinite limit. lim In (x – 2) x-2+

A: Solution is here

Q: 5. Prove lim 5x + 2 = 17. Your work should include pre-work, and formal proof.

A: To solve the following question on limits

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

A:

Q: 44

A: To prove,

Q: 9. Find the indicated limit. lim (6x - 21)³ x-4 = Show any work necessary

A: Solution: As per given data   lim( x tens to 4){ (6x - 21)³} As per simple rule of limit go ahead…

Q: lim does not exist NI

A: Given,  limz→0zz

Q: Prove that lim Vr = 2 using the e-d-definition. Hint: VI - 2 = x - 4 %3D VI+2°

A:

Q: lim (1,4) (0,0) x2 + y2 Prove that

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Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: /2x-1 5. Using defination of limits, prove that lim- Vx-3 %3D

A:

Q: I - 4 Prove that lim vI = 2 using the e-d-definition. Hint: Va - 2 = VT +2

A:

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .