4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x) – 5x %3D (Type a simplified fraction.) II

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Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

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

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

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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: 2x - 6x 34. lim x-0 sin 2x 35. lim 2 1- cos 2

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Q: 2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) –…

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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: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

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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: i) lim cos x-0 7 πCOS²x x²

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

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

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A: Here we have to solve the given limits.

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: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

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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: Vx 6. lim x00 In(x1000) 7. lim 3*-2x X0 x2-x 8. lim 35 sin (nx) cos2 (Tx) 9. lim X-5 2n2(x-5)2

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Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

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…

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

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: x²+1 4.limx→0 x+cosx 1 х3—1 5.limx→1 х-1 9 – x2 maa - 6. lim x→3 V3 + 2x – x² x4-16 7.limx→2 V x³-8

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

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: 5 e 2y sin (- 4x) - lim (х, у) >(0,0) (Type an integer or a simplified fraction.) %3D

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Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

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: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: 1-cos (4x) e) lim x0 2-2cos (6x) (x+1)2 + (2x+3)³ 3x2(8x+1) h) lim X00

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

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

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Q: 2x +5x-3 1. lim 6x -7x + 2 4x-6x+3 lim 16x +8x-7 4. x'+8 7. lim 2x-16 1 -1) h-0 hV1+h 10. lim ) sin…

A: 1) Here, the direct substitution  of the limit value will lead the denominator of the function to be…

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: 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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