sin x cos 4x 32) lim X0 X+X cos 5x

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: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

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Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: O yotan' (x'+3x-s)+ sin (x²s 2x -1)

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

Q: 4. cos*x Evaluate: sin' x( sin' 3/5 x+ cos³ x 3.

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Q: (c) cos lim (tan x)°os x x-(플)-

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Q: lim x-->0 (sin(2x^3))/(3x^2)

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Q: The value of lim sin x- cos x 1s 2 sin x+3 cosx

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Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: Find the limit

A: We have to find out the limit of given function Farmula used- (a-b) (a+b) = a^2-b^2 1-cos2x=sin2x

Q: 1 lim x? sin 1-cos³ x lim X→0 sin² x csc? x-2 lim п cotx-1 4

A: L'hospital rule: If limx→cf(x)g(x)=00 or ∞∞, then limx→cf(x)g(x)=limx→cf'(x)g'(x). Limit formula:…

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

A: In this question we need to find limit of the given function.

Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: tan(5x) (1) lim 40 sin(3x) sin(6x) (2) lim x-0 4x3 – 5x

A: 1) limx_0tan(5x)/sin(3x) 2)limx-0sin(6x)/(4x3-5x).

Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

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Q: 1-cos 2x lim x2 sec x-tan x lim X→0 X→- 2 x- 2 x2 +sin 3x lim 2x+tan 2x . х-0

A: We are solving first question for you. If you want solution for any other question than please…

Q: 22. lim cos2 (x - tan x) cos 2x - 1 sin x 24. lim

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Q: sin( 2 cos (x/ 20 )) = Select one: O 2x (400 - x )°/(400 - 2x) O 40 x/ (400 + x) O ( 2x - 400 ) /…

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Q: x+2 lim sin - x+6x+8 3 2.

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

A: We have to solve

Q: *k) 1- (sinº x+cos x) = 3 sin² x cos²x

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Q: 2 3 lim x2.tan=.sin- x) X-00

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Q: sin 5x. lim X0 5x. Cos 5x

A: Given limit, limx→0sin 5x5x·cos 5x

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: 43. lim x sin(7/x) 45. lim sin 5x csc 3x

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Q: Evaluate the limit.

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Q: 2 sin x lim x→01 – cos x + sin x -

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Q: (1) limx¬(1/2)-(tan x)cos x

A: Given that  1)limx→(π2)-(tanx)cosx 2)limx→0x-3(tan-1x-x)

Q: tan 7x i) lim x+0 sin 3x sin(x2 + 3x + 2) j) lim x+2 x + 2

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Q: 2. sinx+4 sin x-5 lim sin x-1 Xx/2

A: →When limit is of the form 00 or ∞∞, then L Hospital's rule is used. In this rule, take the…

Q: limit x to infinity (1+sin(3/x))^x

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Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: cos(2x)– cosx sin x 4. lim, »o

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Q: 2 lim (x + 6) sin(3x) cot (x² + 6x) X→0

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Q: 1- COs x lim x→0 3x sin x

A: This question is based on limits.

Q: 2cos?x – 1 lim tan(2x) sin 5x lim x→0 lim х-о бxsec(3х) x2 + sin 2x lim cos x – sinx 8x 10x

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Q: Find the limit.

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Q: (7x – 10,* lim x+0 7x lim 2x sin- 9 sin 27x lim x2 21x lim x+00 12 – 3x

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Q: 2) lim sin 4x

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Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

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Q: 4 If cos x = csc x < 0, then sin 2x = cos 2x = tan 2x = ||

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Q: 4.x (a) lim 10 sin 5x sin() (b) lim 5x sin 3x (c) lim 10 x2 tan 2.x

A: Read the following instructions once 1. Short method is provided at the end of the subpart (c)…

Q: = If f(x) = f'(x) = ƒ'(5) = 4 tan x, then - sin(x)-4 sec² (x) Cos x

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

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

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Q: X+ x cos x lim 1- X 0 sin x cos x lim sin 5x sin 4x

A: Formula: limx→0xsinx=1

Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

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Q: cOs x tan x 28) lim x→0 sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2

A: As per our guidelines we need to solve only 3 questions .please repost the remaining subparts as…

Q: Evaluate lim,→0 ela-cos 7x 8 sin x 7

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Q: o( san(s) sin(2x) + lim X 0 cos (x) × 6

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Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

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Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: tan 3x lim sin 8x

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Q: lim cos xx x-0

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Q: tan*(5x) limx→0 x sin³(2x)

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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.