5) Evaluate the following limits x2 lim x→-0 e

Q: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

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Q: 4] Compute the following limits, using the Algebraic Limit Theorem,where (x„) → 0. 1+2x, a) lim…

A: a) lim 1+2xn1+2xn-3x22 Since limit of xn is zero . Using lim cxn=climxn So, lim 2xn=2limxn=20=0…

Q: Use l'Hôpital's rule to find the following limit. 3x-2x lim 3 X o 5x° +3

A: To use the L-Hospital rule to find  Lim(x tends to infinity) [3x³-2x]/[5x³+3]

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: Evaluate the following limits. 1 - cosh x 1. lim x+0+ ln(x² + 1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: х — 1 X - 1. lim ( 1 2x – 1 |4x² – 1| x→2

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Compute the following limits exactly. Vx+22 -10 lim X 78 X-78

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Q: Find the following limit.   Lim  x→0+          ( 2x sec( 3 π/2 - x))

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Q: Determine the following limits analytically.

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Q: Compute the indicated limits. 2x + 5 lim cos 3x? + 2x – 5

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Q: lim (x 1/2 ln x) X→∞

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Q: 4. lim ) ズ→1 Xー1

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Q: Find the limit. lim x-2/In x X x-0+ O -2 O e?

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Q: (c) Find the following limits WITHOUT using the L’Hopital's Rule. -5x2-8 lim x→+∞ 2x+3 (i) Зx+1-сos…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: I. Evaluate the following limits. 1 1 1. lim x→1+ x – 1 er – e - -

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Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x 4/3 X (a) lim x1 x³…

A: According to Bartelby's guidelines we can only solve first three sub-part at a time. Please post…

Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: a In x (b) lim 100 I+ In x

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Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

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Q: 3. Evaluate the following limit. 1 lim x→0* x 1 tan x,

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Q: Evaluate the following limit x3 + 2y³ lim (x,y)→(0,0) x² + 3y²

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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: (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: 2. Determine the following limit. 450 lim x→∞ 9+3 .1.2-0.25x+10

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Q: 15. Find the following limit V2x+5–1 lim x→-2 x+2

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Q: x+cos x b) lim x-∞ x3+3x

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Q: Find the following limit: 6) lim (x – Ln(x² + 1))

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Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: 9) Find the limit. lim f (z) æ – 2| ( (z) = 2- 2 Graph method

A: Since you have asked multiple questions in a single request so we will be answering only first…

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: 2. Compute the following limits: (a) lim -x+ 7x + 3 (b) lim -x* + 7x +3 3 + 7x + 3 (c) lim

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Q: (1) Find the following limit: x2 – 5x+6 - (a) lim x-2 x2 +x-6 ex +e-x - 2 (b) lim x2 In(x) (c) lim X…

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Q: . Prove the following using the epsilon-delta definition of a limit. b. lim x² = 4 X→2

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Q: Evaluate the limit T: x lim cos 4 x+11

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Q: x² + x 1. lim x++∞ e²x + Inx 2. lim (sech 2x) esch x² +0+x

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Q: Evaluate the following limits for h(x) = { 1- 5z 120 (i) lim h(r) (ii) lim h(x) (ii) lim h(z)

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Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: 1 6. lim x++00 x(Vx* + 1 – x²)

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Q: 4 Using the e – 8 definition of limit, prove that lim x→3 3x 1 1 2

A: To prove the limit of given function using the epsilon delta definition of limit which states that…

Q: Find the limits limx→e+(ln x)1/(x-e)

A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

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Q: evaluate the limit.

A: We want to evaluate the following limit.

Q: Evaluate the following limits: x – 25 (i) lim x+25 Vx – 5 Vx² – 3 (iii) lim x→-o 4x +5 sin(50) х — 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the limit. lim x5 In x x-0* O 1 O 5 O-1

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Q: 2. Evaluate the following limits. /x²+3 d. lim X-0- X

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Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

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Q: Find the limit. lim Cn (3+x)- In (l+x)]

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