Compute the following: x2-25 lim x-5 i. x-5 lim sin x 1-cos x ii.

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: b. Evaluate the following limits: 7x cos)-7x lim- [sin(-2x)sin(5x)sin(7x)] lim 5x2 2x cos(x) X-0

A: We write the given limit in the following format

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

A: Let's solve for given limit.

Q: Find the following limits if they exist. 1 lim 1 a) b) sin x-1 lim cos x

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Q: Evaluate the following limits. x + sin(x) + 2vT x + sin(x) V1+x – 1 – 5 a) lim 2 b) lim r2

A: Given: a  limx→∞x+sinx+2xx+sinxb limx→01+x-1-x2x2

Q: Evaluate: 1- cos(x) lim 3x2 X+ 0 Express your answer in 4 decimal places.

A:

Q: Use l’Hôpital’s rule to find the limits

A: The L’Hospitals rule is used to obtain limits of a function when it occurs in the indeterminate form…

Q: - Evaluate only thre tan 30 lim 0 sin 80 x+1 lim X00x2+3 ii. lim,sx.g(x) if lim,s = 2 *+g(x)…

A: Solve only three subparts

Q: 2 dx In evaluating is same as evaluating lim cos ). Determine the value of f(x) if x=0.91 4 C- 2+

A: It is given that, ∫242xx2-4dxandlimc→2+cos-1f(x)c4 It is known that, ∫1xx2-1dx=sec-1x

Q: Evaluate the following limits tan x – sin x sin(x – 2) (a) lim x→0 x(-1+ cos³ 2x) (b) lim x→2 Vx + 3…

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Q: Calculate the following limit: 131). lim(1x)ª sin(5). 13л x→0

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Q: Find the value of each limit: 1- cos x а. lim x→0 x+x b. lim sin(x+ h) – sin(x) h h→0

A:

Q: Compute the following limits if they exist. sec x – 1 (a) lim I0- x – sin a (b) lim I40 x – tan x 2…

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

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

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Q: Evaluate the limit of the following: 1. lim sin 3x X-0 tan 4x 1-cos 2x 2. lim X0 sin 2x x2-x* 3. lim…

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Q: How to evaluate the attached limit.

A: The given limit is,

Q: Choose the correct answer for the following limit sin-1(x) – tan-1(x) lim 3x3

A: For evaluating this limit expression, we will use expansion of inverse trigonometric functions. Then…

Q: Evaluate the following limits: 1. 2 sin x - sin(2x) -x-sin x (a) lim 25 -t2 (b) lim 15 tl 11m,…

A: Hi, since there are multiple sub-parts in the questions posted, we will answer first three subparts.…

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - tan x 2. lim (sin x x→0+

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Q: Evaluate using substitution.

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Q: B. Evaluate only three of the following limits tan 30 lim 0-0 sin 80 x+1 i. ii. lim + zX co-x 1 = 2…

A:

Q: lim = 0 sin x.

A: limx→01x-1sinx=0

Q: Evaluate the following limits: 1 1 (i) lim{ sin -+cos- X X 1/x 1/x +a, 1/x a1 + (ii) lim ..... ,a1…

A:

Q: Find the two limits: sin 2x lim r-T/2 COS x

A:

Q: Q3: Find the following limits if exist:- 1-cos 2x (1) limx-0 sin² x

A: If it is required to evaluate the limit limx→af(x)g(x)=00. That is if applying the limit leads to…

Q: Calculate the following limit: 9.sin(x) lim x +0 10.x

A: Note: Let limx→afx=M, where M is finite and let c be a constant. Then, limx→acfx=climx→afx

Q: Find the limit. sin(x – 3) lim х>3 x* + 5х — 24

A:

Q: Evaluate the following limits: tan 0 1) lim 0-0 02 cot 30 -x* 2) lim x00 x-7 x3+7x²+1 x+3 3) lim x-3…

A: (1) The given limit is: limθ→0tanθθ2cot3θ=limθ→0sinθcosθθ2cos3θsin3θ=limθ→0sinθsin3θθ2cosθcos3θ It…

Q: sin 3x x-0 tan 4x 3. lim

A:

Q: 2. Calculate the following limits: (a) COS x – 1 lim x40 sin x In(1 + x)

A: To find the limit Lim(x tends to 0) [cosx-1]/sinxln(1+x)

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 the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

Q: Calculate the following limits. x² – sin²2x lim X→0 x2

A:

Q: Q 4. (a). Simplify the indicated limits on the following. (CLO-2: LOL 3x²+5 lim X→∞ x2+1 [sinx lim…

A: Q 4. (a) (i) The given expression is limx→∞3x2+5x2+1

Q: Find the following limits: cos( TX) 5. lim 2-x 3x 6. lim tan 1+x V4x²-5 lim 7. x+2

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Q: Evaluate the following limits: x + sinx lim х-оо 2х + 5 lim - х-0 tan3x 1- Vx lim x-1 1 - xX x. Sinx…

A:

Q: Evaluate the following limits. x + sin(x) +2Vã x + sin(x) a) lim

A: NOTE***As per bartleby guidelines for more than one question, only first to be answered send other…

Q: Evaluate the following: Lim(x to 0) (1+x-cosx-sinx)/(x+cosx-sinx-1)

A: This question is related to limit.

Q: Choose the correct answer for the following limit sin-1(x) – tan-1(x) lim x→0 2x3

A:

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - 2. lim (sin x)tan a x→0+

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Q: Choose the correct answer for the following limit sin-1(x) – tan-1(x) lim 3x3 (A)

A:

Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: Evaluate the following limits if they exist. 1 — х — е" a) lim 2(1 — е") b) lim (1 + sin x)'/= sec x…

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Q: Calculate the following limits. cos x 1) lim (tan x)cos* x² – sin?2x 2) lim x→0 x2

A:

Q: Evaluate the following limits: x – 25 (i) lim x+25 Vx – 5 Vx² – 3 (iii) lim x→-o 4x +5 sin(50) х — 3…

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

Q: Q.3/ Find the limits for the following: 1) lim sin 7x 2) lim x0 sin 5x 3) lim V-3 x→9 ズ-9 x1x3-

A: We will find the limit.

Q: 4. Find lim (sin¬ V)cschr. r0+

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

Q: Use the limit lim 0-0 sin e 1 to find the value of lim 0-0 1-cos 0

A: Given limθ→0 θsin θ=1⇒ limθ→0 θ1-cos θ=00

Q: 1-sin x 18. lim TL X- 2.

A: