1 33. lim х>о 2х + sin x

Q: Evaluate the following limits

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Q: 2 lim In (cos x)e

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Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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

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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: (12 sin )( In x) (x3+5)(x-1) Evaluate limx→1

A: Here we have to evaluate the given limit .

Q: If L = lim x-18 x+ sin(+1) 1 + [x/³ ( and M = lim x→0 of L + M + 11. (172) 1 + 1² sin 2x tan-1 dt…

A: Here we will use L'hospital rule     limx→a fxgx  in 00 or ∞∞ form =limx→a f'xg'x   and Lebnize rule…

Q: 1. x² tan( + 47) + 2 tan-1x lim =? (a) 1 (b) -2 (c) -1 (d) (e)

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Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

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Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

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: П 9. In(1+ kx) sin r x(ekz – x – 1) lim \k=2

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Q: 16 |how do you express limn→0 0 Li=1 - (5+ £)9/ as п definite integral

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Q: x[e² 1] Compute lim- x→0 1- coS X

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Q: Find the limit analytically

A: Given, limit function is

Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: tan( xy) lim (х.у) >(0.1) х"у+x = ? 1 (b) 2 1 (c) 3 (a) 0 (e) 1

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Q: 1. 5.lim cos(x) sin(x)

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Q: n lim >(sin (2mx;))Ax over [0,1] i=1

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Q: (d) lim In(cos r) エ→0

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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: Q5 a) 100 5² +2³+ [In(Inr)] lim 1+ 7 +6² + [In (In x)] 200 cos x ln(x - *) *-+*+ In (e² - e*) b) lim

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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: Evaluate lim (2+ y) sin(x). (x,y) → (1,6) 02 O O o O Does not exist

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

A: We need to find limit.

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: 2017 3 Example 9 Prove that lim vx +x² sin = 0.

A: Solution: The objective is to prove the given limit value is 0

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: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

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Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: Evaluate:* x + 4x lim x4x2 + 2x - 8 4/5 1/2 2/3 3/4 Differentiate with respect to x: * y = sec(x² +…

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Q: (b) lim (sin(x) csc(x)) 00 O 100 O c00 O o. 0 O 00 - 00 O not indeterminate 이ㅇ 818

A: sin x .csc x=1

Q: 2 cos (n²+ 3n – 7) - b, Find lim b, V3n² – 4 -

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Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: Q4:Evaluate 1) lim (1-1) x-0 \sin x

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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: х(4+sin 6x) 3. lim X→+0 х+1

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Q: 8. im e* 2x 9. lim e* 10. lim e* x+00 x00 sin 6x 11. lim 5*+6 12. lim

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

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

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Q: in(cos(x)) 2 limy→0

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Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

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Q: Q5 100 5+2³+ [In(In r)] lim a) 1+ 7 +6² + [In(In x)]200 cos x ln(x-7) *-+*+ In (e-e) b) lim

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Q: Find the limit.

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Q: 12 sin( In x) (b) Evaluate lim,→1 3+5)(x-1)

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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.