1 2 Calculate lim x – 1 x² – 1) x→1

Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: 4. Let 1 4- t ift 2 Find the value of c so that lim B (t) exists. t-2

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Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

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Q: Prove that lim x->0 x4cos 2/x =0

A: Important: cos 2θ = 1 - 2sin2 θ

Q: 1. Evaluate the following limits. 3 3 7. (а) lim T x→7 x – 7 x + 3 (b) lim x→-3 V 84+ x – 9 xª – 1…

A: Solve for the limit

Q: 21. If f(x) = In x, then lim f (x) – f(3) is x→3 x – 3 1 (A) (B) e (C) In 3 (D) nonexistent

A: topic - limits

Q: Evaluate the following limits. 1. lim (1+ Vw)(2– u? + 3w) 22 – x - 2 4. lim 6x2 – 7r +1 7. lim エ→ー1…

A: Topic:- limits

Q: 2.15 Suppose there exists a E R such that x > a implies f(x) > 0. Prove: 1 lim f(x) = 0 + lim 0. %3D…

A: We have to prove the given limit.

Q: Find the limit. /h² + 10h + 11 - /11 lim h→0* h² + 10h + 11 - /11 lim h h→0*

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Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

Q: 1 5. Find lim using special limits. X→0 xcot2x

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Q: 4х — 1 4x2 + 3x Find lim f(x) if 5. x2

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Q: 39. Find lim f(x) if, for x > 0, 4x? – 5 4x6 + 3 - < f(x) < x6 x2

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Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

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Q: 1. Find the limit. t² 4 8 lim t-2 +3

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Q: 6. Evaluate the following limits analytically. a. lim 1-4 3x+1 r'- 5x - 6 b. lim 1-6 x - 36 c. lim -…

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Q: 5. Find lim f(x) f(x) 2 1 i -1 2 -2

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Q: (2) Evaluate the following limits a) lim (xt 1)² x2-1

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 3. Evaluate the limit of lim(x² + x + Vx + 1) x→3

A: A limit of a function f(x) is defined as a value, where the function reaches as the limit reaches…

Q: Find (if exists). lim (х,у) — (0,0) (4 + (x² + y²) In(x² + y²; Dose not exist O 4 0 1 0

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Q: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

Q: 3p(x) If p(x)%3х2+2х-З and q(x) -x3- 1, then lim- x+1 q(x)

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Q: 1. Use the definition to establish each of the followii (a) limx→2(2x– 7) = –3 (b) lim→1 T = (c)…

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Q: 19 let ɛ > 0 be arbitrary. Determine & as a function of e 2 In formally proving that lim -x + 8 1/4

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Q: Calculate the following limits x2+4x-12 а) lim x-2 b) lim Vx +1 In(x+ 1) |x-21 X→ー1

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Q: 2- Determine lim[ v( x-1000)+10]/x x-0

A: Given problem:-

Q: Evaluate teh following fucntions

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

Q: (1) Evaluate the indicated limits, if exist (x³ + 1) -x (а) lim r+0 V9 + x² (b) lim In I→1+ (c) lim…

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Q: 18. Find (if exists) * lim (x,y)→(0,0) (4 + (x² + y² ) In(x² + y² )) O 1 O Dose not exist - O 4

A: Limit of the two variables function : Let f be a function of two variables .The limit of f(x,y)…

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim, 3 f (x)=21 x→3 b) limx? -x+1=-5 c) lim x→2…

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Q: Prove lim(Vn+1- n)=c 8. 0 =

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Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

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Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

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Q: 2. Let x+1 r -1 Determine if lim f(x) exists. r-1

A: The objective is to determine if the limit exists or not.

Q: The value of k such that x2 lim kx + 7 x→1 x – 1 exists is

A: Given: The limit expression limx→1x2-kx+7x-1, To determine: The value of k such that the given limit…

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: 1- Find the limits: Vx- 1 lim xI x-1 а. 2x3 b. lim X- o 3(x-2)2 2x3 c. lim X-2 3(x-2)2 x+1 d. lim…

A: Given: a)  limx→1x−1x−1=?b)  limx→∞2x33(x−2)2=?c)  limx→22x33(x−2)2=?d)  limx→3x+1(3−x)2=?

Q: 1 1 Find the limit lim *+5 8 x→3 x-3

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Q: 1 2 Calculate lim x→1 x – 1 x2 – -

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Q: 2 Evaluate the limit lim (Gi)G T-1 I+2 3x +5

A: Here we find the value of limits.

Q: Can i get help with this problem step by step?

A: Calculation:

Q: Evaluate the limit given below. lim 9ti+ 1²-16 1²-4t j+ k 2 (→ 4

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Q: 1 | 1. lim f(x), where f (x) = x→1 x² – 1° f (x) f (x) 1.002 0.998 1.001 0.999 1.0005 0.9995 1.00001…

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Q: Evaluate the limit 1. 1. 10 1. 6. lim - 1 t 1

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Q: 8. Find the following limits: Vx+6-3 lim 91 x-6x? lim а) b) X-3 7+3x x+3

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Q: 2 39. Prove that lim x"cos = O. X-0 X

A: The given limit to be proved is

Q: 4x 7 lim 1+ Compute the limit: x→0

A: here we put value of limit then we calculate

Q: 10. Use the squeeze theorem to find lim f(x) if 2x+2 ≤ f(x) ≤ x² +3. x-1

A: Given: Use the squeeze theorem to find limx→1f(x) if 2x+2≤f(x)≤x2+3

Q: Evaluate I (n +) lim as n → ∞ VnT (n + 1)

A: Given: limn→∞Γn+32nΓn+1

Q: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). Find limx→3 h(x) algebraically

A: h(x) = x2 - 2x -3x2-4x+3 To find :limx→3h(x) limx→3h(x)  =  9 -6-39-12+3     (By direct…