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

Q: - «) lim (2 – ez x→0

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

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Q: 65. lim (cos x)/

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Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: 111. lim cos x -2

A: To find,

Q: -2x lim (e cOs x) х) x → 00

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Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

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Q: 27. lim (x + cos

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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 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X<0. Therefore, Sin(x)<0. Therefore, the…

Q: -3k sin() - cos(;)| for k = 1, 2, ... and let A = lim y00 A(k). Then Let A(k) Select one:

A: We have defined a sequence of matrix as  A(k) =  - 3kSin(1/k) - Cos(1/k) e^( -1/k2 )  e^( -k2 )…

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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

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Q: i) lim e5x cos x 个。 ン

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: By whatever justifiable means, find In(1 – 22) lim sinh z e – In(e – z) - and lim z+0 z – 1+cosh z |

A: To evaluate the given limits

Q: 44. lim sin² x x→n/4

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: 02.) Find the limit lim X+x cos X sin x cos x 1- X→0 lim sin 5x SIn 4x 3-

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Q: 2х + 1 29. lim x² – x X→-∞ - sin 2x 31. lim

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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: 6. Find 1 - cost lim 1+0 t state that it does not exist. e-¹k) o i + tant j + e or

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

A: lim (2x-x2)/sinxx→0

Q: (b) lim (r + 1) In x

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Q: 8. Evaluate e8x - 1 lim sin (6x)

A: See the attachment.

Q: 5 sin(2z) z-40 1- cos(2) Find the limit. lim COS

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Q: (c) lim 1 In x x→0+

A: To find out the limit

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 +…

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Q: 4). limn Jã X 00

A: Given, limx→+∞ x We have to calculate given limit.

Q: I. Evaluate the following limits: sinh(x2−x2) 1. lim x→0 sinh(x−x) 2. lim (x - ln x)* x+0+

A: The given problem is to evaluate the given limits of the given functions by checking the left hand…

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: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: et 1 lim (→0-

A: We need to calculate limx→0-ex-1x

Q: 8 sin((k – 1)x) sin (2x) П ¤(ekz – 1) lim \k=2

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Q: 2 cosh 2, 2 0. Then the lim f(x)

A: Given function is fx=2coshx , x<0sinhx  , x≥0

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: /10-х - 2 8. lim x-2 х+2 А. 1/12 В. -1/12 С. -12 D. DNE

A: The given function is 10-x3-2x+2. We have to find the limit of the given function at x=2.

Q: 73. lim In(cos x)

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Q: (4) Lim + Cos

A: The following limit has been obtained for the given function when x tends infinity in step 2.

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: 4. Find the following limits WITHOUT using the L'Hopital's Ru sin? r lim I-0 1 – cos I i. tan 2r lim…

A: Since you have posted multiple questions i do first three subparts as per our company guidelines…

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: 2x e* –1 lim- x→0 sin (2x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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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