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 4- 5 - lim 4x2+25

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)

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Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

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Q: x²-sin²2x 2) lim x-0 x² 4) lim(1+x) cScx x-0

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

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Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: lim x → ∞ cos(16/x)^(13.32x^2)

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Q: cos x lim X-0 x2-x+3 lim 1-vx-6 x-7 x-7 X+7

A: We have to find out limit

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

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Q: -lim COS X tanx <-2メ X-8 2 lim 3 x→2 x42x +X-2 A

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Q: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

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Q: x-2 2. lim 2 x-8 x+3 5. lim 1/x+1/3 1 8. lim X-1 x-1 11. lim X-0 sin x 14. lim (x-3) cscx

A: We will first discuss the L-Hospitals rule. If the limit of the function is of the following form we…

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: 1-cos 2x lim x→0 x2

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

Q: x cosx-sinx lim x2sinx 1 1/3 3 -1/3 4 -7 2.

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Q: 2x -cos(2x)- 2x - (b) lim | x2

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Q: V3x2 + 6 f) lim x+0 5 - 2x g) lim 4x2 -х + 2х x--0 x2 h) lim x-+0 1- cos2 x tan 7x i) lim x-0 sin 3x…

A: ' According to the guidelines issued by the company we are supposed to answer only first three…

Q: tan 3x 18. lim 1-cos x 19. lim -0 tanx

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

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

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

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

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Q: 1-x c) lim- x1 1-Vx こ 11- sin x d) lim エー→0

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Q: x²+3 1) lim X00 x2+4 1-cos x sin x 2) lim- X-0 sinx 3) lim X-0 ex-1

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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:

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Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

Q: sin(2Tx) lim x → 3 x2 – 9 | O -0.6667 T O 0.6667 T O 0.3333 ↑ О -0.3333 п

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Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

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-sinx x²-49 b. lim x→7 x-7 lim C. lim X→00 x²+1 a. X 1-cosx

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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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: (2-4)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

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Q: 2- x - sinx 1. lim x00 x + cosx x*+2x-1 2. lim-0 x3-2x2+x

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Q: (2-4* limx-1 sin(x³–1) X. x-1

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Q: find lim x-> 0, cos (12x)-1 / 3x

A: Given,              limx→0cos 12x - 13x Move the term 1/3 outside of the limit because it is…

Q: x²+1 4.limx→0 x+cosx 1 х3—1 5.limx→1 х-1 9 – x2 maa - 6. lim x→3 V3 + 2x – x² x4-16 7.limx→2 V x³-8

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: 3 lim tan³ 2x x→0

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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: 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: 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

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Q: 1-cos(2x) tan x-sin x Q6- Evaluate: a- limx-0 b- lim x-0 sin (3x) sin³x

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Q: cos 3x – cos 2x - Evaluate limx→0 x2

A: Consider the given function, limx→0cos3x-cos2xx2 applying the limit to the function we get,…

Q: 2 In(x) c. limx→1 1-ex-I d. limr¬0 sin(x)-x cos(2x)-1

A: We can answer both the question as below.

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: 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: limx¬1 x(1 – cos-) x→1

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Q: 3.1) lim x→0 x³ –4x² sin² x

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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.