1 Evaluate the lim sin x>0

Q: 1 Evaluate: lim sin2(x) 4 TC 6 6.

A:

Q: x + 1 Evaluate lim xS0 1 - cos x

A: We will find the limit by substitution

Q: Find the limits in Exercises

A: limx→∞x+tanx+3x+tanx

Q: 8) Evaluate the limits: a. lim x sin X00 ex-x-1 b. lim x3

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: 5. x sin 3) lim00 x+1

A: limx→∞x5sin5xx4+1=limx→∞ x5sin5xx41+1x4= limx→∞ x sin5x1+1x4 = limx→∞  sin5x1x1+1x4=limx→∞ 5…

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: 2) lim (x – T)tan5

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Q: 65. lim (cos x)/

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Q: Find the one-sided limit

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Q: 1. Find the limit of the following functions: lim 00x/3+ cos x 1-cosx lim X-0 sin2x

A: To find the limit of the given functions

Q: Evaluate the limit. lim (1+ sin(6æ))cot (= ) x →0+ ||

A:

Q: Q1: limx→n tan(x) is X-T

A: The given function is tanxx-π. Evaluate the limit as follows. limx→πtanxx-π=tanππ-π=00 Since 0/0 is…

Q: Find the value of Tx³ + 2. lim [sin x3 + 1 -1 1 O O

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

Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: (:) -*) Evaluate: lim 1 ба" sin 6.

A: Topic-limit calculation

Q: Evaluate lim (sin z)an. 10.

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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Q: (a) lim sih 7x (b) lim x 0 sin 7x x - 9 (c) lim x-9 x - 3

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Q: III. Use Squeeze Theorem to evaluate lim 8478 COS X log x

A: To Evaluate: limx→+∞cosxlog12x by using squeeze theorem:

Q: Find the limit. sin(0) lim e-0 60 + tan(8)

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Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

A:

Q: Q1: limx-→n tan(x) is X-T 1

A: Given, limx→ πtanxx-π

Q: Q\ Find lim tan(x)cos(x) O 2 -1

A: The given limit is of the form ∞0 form. Let L=limx→π2-tan xcos x⇒ln L=ln limx→π2-tan xcos x…

Q: 1 Evaluate lim 1 sin

A: The given limit is limx→∞1sin1x Let x=1/z z=1/x when x tends to infinity z tends to 0

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

A:

Q: tan (x – 2) sin(r – 2)4 Evaluate: lim -

A: we want to find the value of limit   limx→2tan2(x-2)sin(x-2)4

Q: (b) Find the following limits i. lim _(sec x – tan x) sin(2x) ii. lim x-0 tan-'(5x)

A: Given:

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

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Q: 1-sin x Find lim by using L' Hospital's rule x1+ cos 2x

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Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: Prove the shown?

A: we have been given limh→0sin hh=1 and limh→0cos h-1h=0 we have to use the limits to find the…

Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

A:

Q: 3* Evaluate (a) lim sin y and (b) lim x→-I /x + 5

A: To evaluate: a) limy→π3 sin y b) limx→-1 3xx+5

Q: Clearly explain why lim (sin-(t) is equal to 1 and not zero. t+0+

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Q: Evaluate limx=0+ e(1/x)

A:

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

A: See the attachment.

Q: Find x² lim x0 1 - cos x

A: Solved below...

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: Evaluate lim?→0  (1/sin² x)-((sin x)/(x³))

A: Solution: Consider the given limit function is limx→01sin2x-sinxx3 Using the property of the limit…

Q: Example 8 Prove that sin x lim = 0. X00

A: We have given a question they're asking for how do we evaluate limit for sine x over x when x…

Q: 1 Evaluate: lim (1+2 sinh x)+20 x→+∞

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

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Q: Find lim sin (4 T x). I -3

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Q: 68. (x) = sec x %3D lim a. As x- f(x)→ b. As x→2 f(x) → /2

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Q: Evaluate lim sin(x)(x +2) 4 8 3x/2+8/2 8 O Does not exist

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Q: Investigate the following limit. lim x → 0 sin(1pi/x)

A: Consider the given limit limx→0sin1πx, that is, limx→0sinπx.

Q: a + cos bx Find all values of a and b such that lim -1. x2

A:

Q: Find Lim o'sin to Sin 02

A: We use the properties of limit and L'Hopital's Rule to find the limit in the given question.

Q: Find the limit.

A: Let the given limit be L - L = limx→∞ xtan1x            .............(1)L = limx→∞ xtan1x1x×1xL =…

Q: 4. Find lim (sin¬ V)cschr. r0+

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