(d) / 10!n dx 10n a* dx

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

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Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

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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: Evaluate the following limits

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Q: 2 lim In (cos x)e

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

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Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

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Q: 3(1 — с cos x) sæ) 64. lim x→0

A: Just use L'Hospitals rule.

Q: 1-sin t lim 1+cos 2t t- 2

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Q: The area under the entire curve is given by 15 dx. We have 00 15x-3 dx lim 15x-3 dx - lim - 00 lim…

A: The area under the entire curve is given by  ∫1x15x3dx

Q: x sin 4x b. lim x-0 1-cos3x

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Q: 3+9sin' x Evaluate dx using suitable technique. cos x

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Q: 1- cos4x lim→0 5x e N – 1 O 1

A: This is 0/0 form so use L hospital rule and Solve.

Q: 1+3x – cosI 2.) lim tan x

A: limx->01+3x-cosxtanx When we plug in 0 for x then we get…

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

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: 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: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

Q: ¥2/3 6. cos'x sin x dx 5.

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Q: Example 6.24. Show that we cannot use L'Hopital's Rule to evaluate x sin- lim X0 sinx itel'e Pule we…

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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: Find the limits

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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: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

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Q: lim a sin(1/2),

A: Given,           limx→0xsin1x

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: 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: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

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Q: 2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for…

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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: lim + sec"() TT

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Q: 2) lim sin 4x

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Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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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: 9) If y = sin(sinæ), then y' is: x + 2| lim (x +3) I→-2- x + 2

A: See the attachment

Q: In x 6- find lim + 3 + /3x dx 2 Jx 7- find 4 x, +x?)– Inx² -e In 99 dx | In(x 8- find (x+1) In°…

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Q: 7x( cos (4x) – 1) Use l'Hôpital's Rule to evaluate lim sin (5x) – 5x

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Q: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: 13). lim n Sin (号)

A: We find limit of given sequence

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.