4-x 2.2) lim x→2- x² – 3x+2

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

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Q: Finding LimitsIn Exercises 9–14, find the limit or explain why it does not exist.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 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

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Q: Зх-7 (1) lim x--o V4x2+x-11

A: Explanation and solutions is given below....

Q: 3. Show that the largest value of o that can be used for some e > 0 if lim (2+ 5x) = 17 is エ→3 anx"…

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Q: lim [r – In(4x + 7)] x→+0

A: To find the limit

Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: (2 -1) s lim z

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Q: 1. 2. 3. lim 2 tan () lim – () 2-16 (x²–16 x+2 lim х -3 х-2 x →4 2 4. 7. x2 -7x+12 5. lim x →4…

A: Limits are given, we have to the find the given limits

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: |1-x*| 5. lim X-o x(x+1) II

A: Here we solve limits.

Q: 43. Assuming that lim 4 = 1, which of the following statements is necessarily true? Why? (a) f(0) =…

A: Consider a f0=0Here if x=0 , f0=0Substituting in limx→0fxx=00Inderterminant formDifferentiate…

Q: 2n +1 a) Using the definition, show that lim n00 3n +4 3

A: Given,           limn→∞2n+13n+4=23

Q: 10. lim( +1-V +1-)

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Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

Q: (금 1 Evaluate L = lim T→2 + x² – 5x + 6 -

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Q: lim x In(2x) x→0+

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Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: lim Vn² +n –n=0 -

A: Given Lim n-infinity √(n²+n) -n When we pit n is infinity directly we found a infinity-infinity form…

Q: lim (- %3D x2 - 2sinx + 2x O 1 42

A:

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: 2sin x lim -0 e - 1 lim - 5 cos x o e - x - 1 4 - 4e* lim -0 xe

A: As per our guidelines, we are allowed to answer the first question only please resubmit the other…

Q: 2n j3 lim - 24n n00 j=1

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Q: 1. 2. 3. () ) lim lim 2 tan lim (x²–16) x+2 - x →4 4-x х -3 х-2

A: Note : According to our answering guidelines we have to solve only 3 sub parts (if multiple subparts…

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

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Q: (3) Evaluate lim -(1+sin(4))t dt

A:

Q: Prove the limit doesn't exist

A: cc

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

Q: السؤال 1 lim iz?-z z-- z2-1 i o -i O 1 0 -1 O

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Q: a lim 6. *a Jx- Ja -x

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Q: (b) lim (r + 1) In x

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Q: 2- -2 (a) lim h(x) 4 (b) lim x--3* h(x) 4 (c) lim h(x) x--3 (d) -3 h(-3) (e) lim h(x) x-0 (f) lim…

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

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Q: x2 -x-2 lim n) 2 x2- 2x X-2 x +5 lim X2 x-3 (o

A: according to a guideline we should have been able to do only one question at a time #n #o

Q: 3x²+2x+1 Q1: Using the L Hopital Rule Evaluate: lim x→0o 5x2+3x+3

A: Given: limx→∞3x2+2x+15x2+3x+3  ……1

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: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: lim (2,y)+(0,0) In(2 + x² + y?) x2 + y?

A: We have to solve given limit:

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: 4x 7 lim 1+ Compute the limit: x→0

A: here we put value of limit then we calculate

Q: ni eoulav sd no 2x + 5 13. lim x→-2+\x + 1八 +x ber

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Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: Using e – N description to prove that lim = 2. n2 +1

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Q: 2n2 + n (a) Using the definition (i.e. N, ), prove that lim 4n2 2 112

A:

Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…