xª – 16 85. lim I-2 X - 2 x - x? – 5x – 3 86. lim X--1 (x + 1)2 VI+x- 1 87. lim х x? – 9 88. lim X-3 x² + 7 4. Cosx 89. lim x sinx 2r 90. lim 3 cosx

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

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Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

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Q: (а) lim 1-cos() 3x 1/х 1/х (b) lim хе 1/х (Hint: хe x+0"

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Q: 4 2 dx In evaluating √ √²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if…

A:

Q: 1- r + In (x) lim 41 1+ cos (3a x)

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Q: 3(1 — с cos x) sæ) 64. lim x→0

A: Just use L'Hospitals rule.

Q: 1-sin t lim 1+cos 2t t- 2

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Q: 23 + 6x² – 32 1. lim 4 x3 + 5x² + 4x bw e 2. lim w>-00 4+ e 3w sin(6t) 3. lim 40 sin(11t)

A: Given that limit problem and we solve use L'hospital rule . If we apply limit and function is 0/0…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16. lim x2 cos(2nx) = 0 %3D

A: As per our guidelines we are supposed to answer only one question

Q: 0/0 form Evaluate the following limits using l’Hôpital’s Rule.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: (a) lim sin 3x x-0 sin? 5x (b) lim x-0 x2 (c) lim tan?x x-0 x2 cos? x - 1 (d) lim x2 cos?7x - 1 (e)…

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Q: find the one-sided limit

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

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A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: cos x lim z-n/2 sin (2x)

A: If limx→afxgx is in 00 form or ∞∞ form; then applying L Hospitals' rule we get:…

Q: 1 25. lim (x,y)→(4,0) (x² – 16) cos (x – 4)² + y²

A:

Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

Q: In Problems 7–16, use a table to find the indicated limit

A: The given expression is limx→24x3

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Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: TOLLOWLNY tan x+ 4 tan 2x - 3 tan 3X Lim x°tanx i)lim| cos-cos COS ....coS

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Q: 12:28 AM Fri Oct 23 77% T +: 0 the formul a, = lim f Cath) - fla) an m tan +o find 3 equation for…

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Q: O Lim tanx メーンク メ と5 5+s2 2Lim S+1 ン4 3) Lim 3-→ yリアンチアン49 6+ )Lim I+ Cos メ→

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Q: tan? x – x? 1 Ans. 12 2 Ans. 3 x + 2 cosx - 2 (xii) lim x0 x2 (xi) lim x sin' x tan x e* + sin x -1…

A: As per bartleby guidelines, for more than one question, first one needs to be solved and others are…

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…

Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: 2x? — х — 1 lim b) х--1 4 — 3x? — х x² + 3x +1 lim x→-1 2x? – 3x – 5 а) VE- 2 m³ – 8m + 1 lim lim -…

A: e)

Q: 60. Does knowing that 2|xy| x²y? < 4 – 4 cos V|xy| < 2|xy|| tell you anything about 4 – 4 cos V]xy|,…

A: According to the given information, the given fact is:

Q: (급-) 금- 1 2 lim 1-x 1-a2 a. x 1 lim x→1(1 1- x- 21- x 2) 2 cos? x+3 cos x-2 lim xT/3 2 cos x-1 (This…

A: we have to find limit

Q: sin(4z) f(x) = 9x 0.4 0.35 0.3 0.25 0/5 -0.25 0.25 sin(4x) Evaluate lim 9x Enter at least 3 decimal…

A: Let's find.

Q: (c) lim sin 3r sin 2r I sin 5z 8r-3 2r³ +z+1 (d) lim

A: Given that:                        (c) limx→0sin(3x).sin(2x)x.sin(5x)(d)limx→∞8x2-32x2+x+1

Q: Q 42

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Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: Vz²+7-3 11. lim,→3 I+3 12. lim,0 sin 3z cos 3z-cos z 13. lim,→0

A: As per our guidelines we are allowed to answer only three subparts of a question. Kindly repost the…

Q: xe* 33. lim e-3r 35. lim 1+00 x+ 3x+1 log, x 37. lim X+0+ log, 3x In(x – 2) 39. lim In(x² – 4) X+2+…

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Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: 35. [T] lim sin2x; ±0.1, +0.01, +0.001, +.0001 *40 X X -0.1 -0.01 -0.001 -0.0001 sin 2x a. b. d. X…

A: The answer is given below:

Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

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Q: AWO Lim tanx L Szx Lim X-CSc メーラク メ メラ。 OLim ()) S→の 6 Lim di6-X +1XI メー→ロ y4 (3) Lim J→ y2ラッチアy49 4…

A: 1. limx→0tan xx2. limS→∞SS+1S25+S23. limy→∞y4y4-7y3+7y2+9 Note:    Multiple parts are given, we are…

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: x² – 9 2. lim x →- 3- x+3 (4 + h)² – 16 4. lim h-0 h sin2x 6. lim t tan³x

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Q: sin 21 lim 2t

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Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: 9) If y = sin(sinæ), then y' is: x + 2| lim (x +3) I→-2- x + 2

A: See the attachment

Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

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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: 1. y = x - x'cosx + 2xsinx + 2cosx 2sim x-1 2. y= cosx+2 3. tan(xy) + xy = 0 4. y= x 5. y = xArctanx…

A: The given function is y=xcosx. We know that duvdx=udvdx+vdudx.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.