What is the value of lim (1+ 4 )": п 4n O-1+i V2 O 1+i V2 O -1-i V2 1-i V2

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: Evaluate the limit. 2² 4x+3 lim,>∞ 3x³ - 2x+3 01 O 1/3 0:3

A: Given: limx→∞ x2-4x+33x3-2x+3  To find: Value of the limit.

Q: 2) lim () – X-00

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Q: Use the fact that lim,ex = c and the result of Exercise 2 to show that lim,c X" = c" for any integer…

A: If the function is a simple function, the substitution of the point of limit into the function helps…

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

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Q: 7. Use L'H rule to find (a). lim (- ), (b). lim rInz?

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Q: use L'HOSpital's rule ro show that lim 2tanx イ→ % rc 2x

A: We have to proof

Q: Evaluate the limit x – 4 | lim 2--1 8x2 – 3x + 8

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Q: (b) With the help of Sandwich theorem (or Squeeze theorem), show that lim (2 √√x - 1)" = x² for x ≥…

A: By using Sandwich theorem,  we have to show that ;   limn→∞2xn-1n = x2  for x≥1

Q: sec x lim sec(3x)

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Q: What is lim In x? x→2

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Q: Evaluate the limit: lim 7x2 cos(2x) - 7

A: we have to evaluate , limx→-π77x2cos(2x)

Q: 5. Use the Squeeze Theorem to evaluate lim sinz 1-00

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the limits i 63. lim x In x 64. lim x(Inx)?

A: Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2?

A: We have to find the lim inf and lim sup of sequence

Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

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: what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8

A:

Q: Which property of f(x) = x' allows us to conclude that lim x = 8? x+2

A: f(x) =x3

Q: . Use the definition of limit to prove lim = 2r - 3 = 7.. %3D %3D

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Q: Lim. 341 そ→+ 6. Find:, 2. -im

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Q: Use the e-d definition to show that lim /a = 2. a-b (Hint: Vā – V6 =

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Q: Find the limits in Exercise

A: Given, limx→-12x3-5x2+3x+5 function is continous so find limit of function at x=-1…

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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

A: We have to prove the given limit.

Q: lim (3x + 5) = 2, x→-1

A:

Q: Prove the statement using the ɛ, d definition of a limit. 1. lim (x² – 4x +5) = 1 x→2 2. lim (x² –…

A: use the definition of epsilon and delta definition  to prove the limit.

Q: The value of lim (trorozac) 2 (1² 1px (ozoz-ozoz) 6202 (17073— 170741) 7 is equal to

A: The property of exponents is anam=an-m. The property of exponents when the exponents are in…

Q: Evaluate using substitution.

A: limx→-π23sin x

Q: find the limit or explain why it does not exist. lim 12 In (2 – Vi) -

A: We have to evaluate the following limit: limt→1t2ln2-t

Q: Evaluate the indicated limits 3z – 5z² + 7 (i) lim 1-400 8+ 2x – 5x4 lim

A: To find: limit of the given function

Q: Use the Squeeze Theorem to evaluate [2 lim cCs X x +3

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Q: Use the e-8 definition to show that lim VI = 2. Z-14

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Q: lim (r + 4x? + 4x – 1) = -1, x-2

A:

Q: 2) lim X+1-x1 メーーt メーー 2x+2

A:

Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: Use the e-d definition to show that lim x2 I→2

A: In this question we will use basic of calculus i.e basic of limits. We will simply find the limiting…

Q: Which property of f(x) = x' allows us to conclude that lim x- 8?

A: f(x)=x3 is a continuous function. So, it is continuous at x=2 also.

Q: Evaluate the limit. 4 lim + 2 (x + 3)? x → – 3

A: Consider the given limit, limx→-3-4x+32+2 now, apply the rule of the limit that is the limit of a…

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

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

A:

Q: What is lim (x? – 4x + 5)? O 1 O 2 O does not exist

A: To find÷limx→2 x2-4x+5    limx→2 x2-4x+5=22-42+5                           =4-8+5…

Q: If /6 – 5x2 sf(x)sV6-x² for - 1sxs1, find lim f(x). N6-5x² lim f(x) = X→0 (Type an exact answer,…

A: Solve by taking limit both side

Q: Does the limit |r +1| lim 1-1 r+1 exist? If yes, find its value, if not - explain why. Show all the…

A: We need to show that limx→ -1x+1x+1 doesn't exist. So,               limx→ -1+x+1x+1x+1 is positive…

Q: Find the limit. 4et – 4 1 + t – 1 2 - - lim 1 + t,

A: When limit is of the form 00 or ∞∞, then L'Hospital rule is used. In this rule,take the derivative…

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

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

Q: What is the lim x². In(x) x-0+

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Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

A: