2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) – 6x %3D (Type a simplified fraction.)

Q: X- 2 sin 5x 1. lim x2 x-4 2. lim 70 5x2-3x x'-1 4. lim 114r 3. lim X00 7x + 1 7)

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Q: arctan(kx) e2x – 1 lim \k=1

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Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

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Q: 3x+7 sin2x x+x.cosx 1- lim- x2-2 lim 2x2+x 3 - lim- x→0 2 - 00+X x→0 sinx.cosx 1 lim x-1- 1-x2 x-3…

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Q: ,- 3y sin (4x) - 3y - 2 e sin (4x) Find lim - 4x (х,у)—> (0,0) - 2 e sin (4x) lim - 4x (х,у) — (0,0)…

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Q: arctan(kx) e2x – 1 lim k=1

A: To evaluate, limx→0∑k=18arctankxe2x-1 Then, the above expression can be re-written as,…

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: lim x → ∞ cos(16/x)^(13.32x^2)

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Q: 2 tan(x)–2x Use L'Hopital's rule to find f (x) = lim 5x3 Note: Retain any fractions in your answer.

A: f(x) = lim(x->0) (2tanx - 2x)/ 5x3 If any limit takes the indeterminate form 0/0, we can use L'…

Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: lim x-0 (cos20x) 7/20x^2

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Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

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Q: x + 3 6x2 + x - 1 41. lim x-3 x +x – 6 42. lim x→(-1/2)* 4x² - 4x - 3 43. lim 44. lim 6 45. lim x→-4…

A: We will evaluate this limits by using one sided limit as shown below

Q: 2x2 – x – 3 (d) lim x→-1 x² + 5x + 4 2x – 8 (e) lim r→4 x2 – 8x + 16 x2 (f) lim r--2 2x + 4

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Q: Find the Taylor polynomial of degree 4 for cos(x), for æ near o: P4(x) = 1-x^2/2+x^4/24 Approximate…

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Q: 1 4. lim %3D x→0 x²(x + 7)

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Q: 1 COS X 13. lim- ズ→0 14. lim e -3x+4 15. lim 4x+7 ー-00

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Q: 44. lim sin² x x→n/4

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Q: 3/x – 3 (k) limx→-∞ 5 - x x³ +1 (1) limx→-∞ Cos -0- x6 +x5 + 100

A: For (k), We need to find limx→ -∞ x-35-x3. So,            limx→ -∞ x-35-x3We know that,…

Q: How to do a problem use Limits? Number 17

A: Here a function in variable x is given and we need to determine its value when x tends to . This is…

Q: Limits at infinity Evaluate the following limits or state thatthey do not exist.

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: 1 + cos(x) a) lim %3D 20 -x ) lim x-1( In(61x-60)

A: Given, limx->π (1+ cos (x))/(6(x-π)²) = (1/6)limx->π (1+ cos (x))/((x-π)²) = (1/6)limx->π…

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: With partial fraction decomposition the following rational expression can be as 110 A B (æ + 3)(x2 +…

A: Given 110(x+3)(x2+2)=Ax+3+Bx2+2

Q: 2х + 1 29. lim x² – x X→-∞ - sin 2x 31. lim

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Q: 6.The lim x +3 is equal to 1S 3x-4x+n sin t. 7.The [1 is equal to

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: 4) Let fn(x) = nx". (a) Show limn→∞ fn(x) = 0 for x ≥ [0, 1). 1 (b) Show limn→∞ ₁¹ fn(x)dx = 1.

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Q: -5x + cos (9x) – 1 Evaluate lim 2x Submit an exact answer.

A: To Evaluatelimx→0-5x+cos(9x)-12x Replace x with 0 in the given expression. If indeterminant form is…

Q: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

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Q: arctan (Vx) dx

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Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: 8. Evaluate e8x - 1 lim sin (6x)

A: See the attachment.

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: 1 1 X sin x+sin 2x Q3/ Find the value of (x) if5 -2 1= lim 3x -1 1

A: See the attachment

Q: 18. L6. 4- x² lim lim x² + 3 x→2 3- vx²+5 lim (2x x →2 x →0 21. 19. 20. lim v25 – x2 lim 12 sin (÷)…

A: We have to find out limit

Q: 2.r + x sin 3.x 1. lim * 5x - 2x +1

A: Here we find limit

Q: (1) x3 – - 13x + 12 5- V4 + 3x lim lim x-3 x3-14x + 15 (3) 7- x x-7 2x*- 6x3 + x2 +3 2x2 - 3x lim…

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Q: -5y 2 e sin (- 5x) Find lim 3x (x.y)-(0,0) 2 e-5y sin (- 5x) lim 3x (x.y)-(0,0) (Type an integer or…

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Q: 1. lim (2r + 5) 2. lim (10 3x) X12 3. lim(-x + 5xr 2) 4. im (x'-2r? + 4x + 8) 5. lim 8(t - 5)(t-7)…

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Q: In cos 2.x 4. Find lim -0 In cos 3x

A: limx→0ln (cos 2x)ln(cos 3x)Applying L'hospital rule:= limx→0ddxln(cos 2x)ddxln(cos 3x)= limx→0…

Q: 4xy lim Compute the (xy) (0,0)

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Q: х(4+sin 6x) 3. lim X→+0 х+1

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Q: In cos 5x Find lim x-0 In cos 4.x

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Q: In x i) lim 1→1 x² + 2x – 3 ii) lim r(, – arctan r) iii) lim z40+ iv) lim xº

A: TO EVALUATE THE FOLLOWING LIMITS CONCEPT USED L' HOSPITAL'S RULE limx→a f(x)g(x)    if  limx→af(x) =…

Q: b-4+ Jb 3x(x – 4) Answer "True" or "False" for the following: In(x – 1) Ji 3x(x – 4) In(x – 1) |…

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Q: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

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Q: X-2 lim = 2 a. By L'Hopital's Rule, x→² X²-1 1 1 lim = x→2 2x 4

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