Which of the following limits is in an indeterminate form? Select all that apply. sin x lim х—1 х — 1 ex — х — 1 lim x→0 x2 x² – 5x + 4 lim x-4 х — 4 lim x→0+ x² – 2x + 1 lim x→-1- х+1

Q: Evaluate the following limits by constructing the table of values. 1-cos(3t) 1. lim- t-0 3t f(t)…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: b. Evaluate the following limits: 7x cos)-7x lim- [sin(-2x)sin(5x)sin(7x)] lim 5x2 2x cos(x) X-0

A: We write the given limit in the following format

Q: Evaluate the following limits by constructing the table of values. 1-cos(3t) 1. lim- t-0 3t f(). 1-…

A: 2. As you have asked for the solution of question 2 only, so I am solving that. Thank you. A…

Q: 1- Evaluate the limit a-Lim(x/(x-1)-1/ Inx) x-1+ d- lim x+1/√2x²+x+1 x-→∞ b- lim [In(cos(x))]…

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Q: Match the values on the top with the given limit. A -o BO C 8/9 D +co 9 x2+12 x +9 lim 64 - x2 X- 8-…

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Q: 4.) Evaluate the following limits at infinity. If the limit is infinite specify whether it is plus…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.…

Q: Which of the following limits will be indeterminate/undefined value when direct substitution is…

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Q: sin2z+7z2±2z 4. lim X-2 z2 (z+1)2

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Q: 1. Determine whether or not each of the following limits exists as a real number or as +oo or -oo.…

A: According to the given information it is needed to check whether the limit of the following…

Q: 1) Find the following limits. Do not apply L'Hospital's rule. x² +x – 6 lim 142 r2 - 2r (a) sin(1 –…

A: 1) a) From the given problem:   limx→2x2+x-6x2-2x   Simply we can write as:…

Q: 1. Evaluate the following limits. - 2 lim a.+2 -4 V2 +1-2 lim b. i+2 t-2 | sin 7r lim c.0 sin 3r

A: As per as our guideline i am supposed to solve only 3 part of question 1 . And f getting solution of…

Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

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Q: 10. Determine which of the following limits exist and does not exist. a. b. 2 - 2 3x - 9 lim 25 * +5…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 9. Use the squeeze theorem to evaluate lim(x – 1)²ecos (Hint: X-1 -1< cos s s 1, x # 1) ズー1

A: If h(x) &lt;=f(x) &lt;=g(x)

Q: 3. Compute each of the given limits. 1 1 1 1 + 3 2+ 1 a) lim ( x2 cos c) lim n-00 n 2 2+- 2+ 2+ | 27…

A: We have to find given limits.

Q: 6. Evaluate the limits. sin(0-4) а. lim Ө-0 Ө-4 4w b. im woo 20w+1

A: It is required to calculate the limits of the following expressions:For part (a):

Q: to evaluate the limit. 3 1 v 78. lim x→ x Jo im In(1 + e') di | In(1 + e') dt 2

A: Answer is  1/2 Explanation is given below

Q: 4. lim ¹-cos 2x x-0 sin 2x

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Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

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Q: Show that Hint: Use to obtain In[|x|] √√2/T. 1 - cos(sx) x² 8 1 - cos" x x² lim n-√√n 00 2 π dx |s|…

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Q: 3.lim X→π In(cos2x) (π - x)²

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Q: B. Evaluate only three of the following limits tan 30 lim 0-0 sin 80 x+1 i. ii. lim + zX co-x 1 = 2…

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Q: II. Apply the limit laws on the following: lim (Vx/VA) 2. X+1 cos x x5+ lim X-3 3. X-1

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Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

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Q: 1. Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 - x im x² – 4 sin 2x…

A: Find the limit of the given function  1) (2-x)/(x2-4) , when x tends to 2 .  2) sin(2x)/sin(3x) ,…

Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,oo fn(x) exist for every r E [0, 1]?

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Q: Vx + 32 - 5 Limit. lim x--7 X + 7 O 0.1 O Does Not Exist (DNE or tco) O 10 O 1.4 O 5

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Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: Compute the following limits. Algebraically 1 1 3 x cosʻ x-1 (a) lim x→3 x-3 (b) lim identity c) Lim…

A: Using rules of limits.

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: 2. Evaluate the following limit. 1/x lim (1– sin 3x)"* x→0*

A: Given, limx→0+1-sin3x1x    We have to evaluate this limit

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

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Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: 1. In each of the following cases, evaluate the given limit. x2 +5x 14 lim エー→2 - (a) x2 - 2x t - 1…

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Q: 2. Evaluate the following limit. lim (1– sin 3x)"* x-0*

A: It is in indeterminant form so we have to take log on both sides

Q: Which of the following limits requires L'Hopitaľs Rule to evaluate? O A. x-2 lim 2x -2 O B. lim e…

A: According to L'Hospital Rule

Q: Q2: Evaluate each of the following limits: 1-cos 3X 2)limx-0 9X2 x$sin 3) lim00 x*+1

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Q: Q2/ Find the following limits: 3- 5/27+81 x--00 2/12+Vt²-167 A. lim 1 В. lim-1 x+1 1-sin t С. lim #…

A: We have to find the limit of the following... A. limx→-∞t13-5t2+81142t2+t23-1612B.…

Q: 6) Use the Squeeze Theorem to evaluate the following limits. (a) lim z cos(207æ) (b) lim f(x) if 1 <…

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Q: 1. Evaluate the following limits: x2 V2x2 + 1 Vx2 + 5 (a) (3 marks) lim (b) (4 marks) lim a→3 2* +…

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Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: sin²(2x) lim 1-sin² x 2 lim (2x – 1)vx + 4

A: To find the given limits.

Q: 2. Determine the infinite (∞ or -0) limit as follows: x² – 2 - (a) lim x2- x2 3x + 2 - 4-6 sin x – 1…

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Q: Let fn → f, where if 0 <x < L3 (3 – x) if 1 < x<1 { fn (x) п-3 if 0 < x < 1 - and f(x) if x = 0 Then…

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Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

Q: Find the limit 1- sin z In (100r² + e*) (a) lim (b) lim 1+ cos 2r 100z

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Q: Use L'Hospital's rule to find the limits of the following: a.) (ex-1-x2+x-1)/(x2-2x+1) as x…

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Q: Which of the following limits does not yield an indeterminate form? a.limx→0 3x^2/x−sinx b.limx→2…

A: (a)lim(x→0) (3x2)(x-sin⁡x)=00form(indeterminant form)(b)lim(x→2) lnx2(x2-5x+6)=00form…

Q: h of the following limits analytically; show your work: O LIVE 9-(3-h)2 (a) limp-0 1 1 (b) limx-1…

A: Please refer the attached image for complete solution.