* - 7 I- 5 25. lim 5 x(x - 5)? 26. lim -5* x + 5 4 u - 1 28. lim 27. lim 3" x" 3x 0* sin u 2 29. lim " tan x

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

A:

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…

A:

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)…

A:

Q: 1-cos (x-7) lim ثم اختر الاجابة الصحيحة؟ أحسب الغاية التالية xt (x-n)sin (x-7)

A: We will use the limit theorems to evaluate the limit as x tends to π.

Q: lim (cos(9x)) (+) +0+x

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Q: x + 2 (16. lim x→-3- x + 3 18. lim cot x x? – 2x 20. lim .2 x→2- x² 4х + 4 Зх + 5 22) lim x→0 x – 4…

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Q: lim x → ∞ cos(16/x)^(13.32x^2)

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Q: 1- cos(2x) lim x→0 х-0 1 — сos(6х) 7* – 6* – 1 lim x→1 х2 — 1

A:

Q: {) Lim 1-cos Scos2x 7 メー)○ x2

A: Given: limx→01-cosxcos2xx2 for evaluating given limit, we use L hospital's rule according to L…

Q: x2-4 1) lim x→2 x-2 sin 2x 2) lim 3) lime- 1 x 0-x

A:

Q: 16. lim (2 – 3x) = –4 x → 2 %3D - 19. lim (1-3-) -- 3 20. lim 2 = 7 x → 5 21. lim x2 – 2x – 8 = 6 x…

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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…

Q: 13) lim (n z 2-70 24) lim e- é- ース x - sinx 34) lim (Csx - Cotx)

A: Wherever applicable we used L'Hopital rule

Q: i) lim cos x-0 7 πCOS²x x²

A:

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: 5. lim 16. lim 0 V3h + 1+1 0 Vsh + 4 + 2 3h + 1- V Sh + 4 - 2 7. lim 18. lim

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Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

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Q: (а) 1- cos 4x lim x? x-0 5-х (b) lim- 45 Vx-1-/2x-6 312 -t- 2 lim 1² -1 (с)

A:

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

A:

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

A:

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

A: The given expression is limx→24x3

Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

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: 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: cos(7x) – cos(9æ) lim x2

A:

Q: Зх + 1 1 lim x→0 sin x 5 2 3 1 2

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Q: 4.x - 1.) lim 32 1 — ебх-12 1+ 3x – cos x 2.) lim tan x

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Q: xn²+1. lim, cos( x0 cos(*+1) x² +3 limx→0+ *国

A:

Q: 4. lim -0 A. -2/2 B. 1 C. 2 h D. Does not exist sin

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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: lim -7 tan x X→(11r/2)

A: solution given below

Q: Limits at infinity Evaluate the following limits.

A: "Since, you have asked a question with multiple subparts, we will solve the first three for you. If…

Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is…

Q: x+1-cos²(x) 3sin(x) 7. Find lim

A:

Q: S 1. lim 2 I- I - 2 1.9 1.99 1.990 2,001201 | 21. 12 2, lim 19 1.99 1.999 201 1211

A: Please see the explanation below

Q: 3 lim z? sin(-

A:

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

A:

Q: Evaluating limits Determine the following limits analytically

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

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 3) lim(-- x0 x V

A:

Q: 35. lim (sec 2/2 x – tan æ)

A:

Q: 2 sin(z) – sin(2z) lim -10 z- sin(z)

A: We use L'Hospital rule to solve this limit problem.

Q: 1+3x COS x - 2.) lim tan x

A:

Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

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Q: V+12-4 3 .lim X-2 tan3x 2. lim X-0 sinax 4). lim X00 x-7x+1 x-2

A:

Q: lim COS X tanx メー→o <-2メ4リX-8 2lim 3 メ→ 2 xリ_2X メ-2 xツ_2Xメ

A:

Q: 1 lim(x²-3x+1) 3. lim tan(x²) 7. lim 2²-1-2 x²-4

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

A:

Q: lim cos xx x-0

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.