33. lim (2x + 3) 34. lim (4 - 2x) x-2 37. lim sin x x/2* 38. lim (3 cos x) x – 1 x³ - x? 41. lim x-1 x + 1 42. lim x-0* x + x2

Q: X- 2 sin 5x 1. lim x2 x-4 2. lim 70 5x2-3x x'-1 4. lim 114r 3. lim X00 7x + 1 7)

A:

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

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: lim x → ∞ cos(16/x)^(13.32x^2)

A:

Q: 25-и-5 e. lim u-0 vi+u-1 f. lim (3x² + 1)-2 x--00 2x? g. lim X+0o x²+1 x3+x

A: To evaluate the limit: e). limu→025-u-51+u-1 It is 00 form. We will evaluate the limit using…

Q: determine the lim_{x->0} cos(2x)/x - determine the limit_{x->0} sin(2x^2)/xtan(4x)

A: Consider the given limit, limx→0cos2xx the left-hand limit of the function will be, since the…

Q: COs x lim 1 (b) In(2/9) – In(x(1 – x)) x – 2/3 - - lim x→2/3 (c) lim r(tan x2 - In x lim x0+ x In(1+…

A:

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: 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: Can you solve number 23

A: The given expression:

Q: x? 16. lim 0 1- cos x 1+ cos 0 18. lim 0 1- cos 0 x + x? 20. lim x- 1- 2x²

A:

Q: 1. lim In (x –9) 2. lim log, (8x-x*) x3* x-2" 3. lim In (cos x) 4. lim In (sin x)

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: 5. Evaluate lim sin(x)– (x² + 3x – e*). (x³ – 2x2 - 6 + 3x) 6. Evaluate lim X→2 х - 2

A:

Q: Please solve asap my deadline is very close

A: We need to find limx→+∞sinx-4cosx+33x2+cos2x Consider:…

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: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

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

A:

Q: 1) lim X-2 2x-4n x(1-cosx) 2) lim х-0 tan(tan?x)

A:

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: 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: 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: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

A:

Q: 1 3. lim coS x 14. x-0 5. lim 4x+7

A: Given query is to find indicated limits.

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

Q: 1 - cos b. lim COS x 1 x0cos x 1 20. a. lim x0COs x 1 a inil ol l

A: Given information:The given limit function is shown below:a)

Q: cos x-2sinx 1. limx-n 3cosx -2 limx-3 X-3 3x6-x*+2x-3 limy--o 4x5+2x3-5 iv. lim,→-1(x³ limy--1(x³ –…

A: [i]

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+

A:

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: 4-V16+h 9. lim x+sin x 12. lim

A: Note: As per bartleby guidelines for more than one questions asked only one question is to be…

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

A:

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

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

A:

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

A:

Q: 1. Lim 2×ー2xーメ+1 x-x3- 2x + 2 3. Lim メ→。 |- Cos X X-1 Sin 2x 2. Lim csc ax Csc 2x 4. Lim 7X 2x+5 x-…

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Q: limit as x approaches 0 of x^6*cos(4/x)

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Q: 2 sin x-sin 2x lim х-sin x 3 O -3 6 -6 о O O

A: Given- limx→02sinx-sin2xx-sinx To Find- The valuie of the limit.

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

A:

Q: 1 lim, (e** - 1)sin-+9cos x . x0

A: Given: limx→0ex2-1sin1x+9cosx we know that  limx→0ex2-1=0 and  limx→0sin1x=-1 to 1 so,…

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: x2 h) lim - x+0 1- cos?2 x tan 7x i) lim X-0 sin 3x sin(x? + 3x + 2) ji) lim x+ 2

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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: x*cos (x²) 1 – cos 3x lim X-0

A: we have to find the limit of the given expression

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.