) lim- 1 5 arctan -4arctan |=? Use L'Hospital's Rule 4 X-0 xVx

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

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Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

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Q: 1 5 arctan x/ = ? Use L'Hospital's Rule 4 lim 4 arctan-

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Q: 1- cos(2x) lim x→0 х-0 1 — сos(6х) 7* – 6* – 1 lim x→1 х2 — 1

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Q: Determine the limit: 12 x+ 1 tan(2 x) lim 3 sin(3 x) X- 0

A: Given limit: limx→012x+1tan2x3sin3x

Q: sin(4x) 8. Compute lim x-0 tan(3x)

A: The solution are next step

Q: 3n Find lim„→∞ (1+)" . Hint: Apply L'Hopital's rule.

A: Please refer the attached image for complete solution.

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: 5. lim X-0 e2x-1

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Q: 1) lim (1--)*

A: As per our guidelines we can solve only 1 question. The rest can be reposted.    In question  no 1…

Q: Which theorem shall be used to find the lim sin 60 0-0 20 Theorem 1:lim Sin X x-0 x 1 = 1

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Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

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Q: solve using L'Hopital's Rule 4. Lim    [ (sqrt root of 2+x2) / x ] π   x->∞

A: To find: The limit of limx→∞2+x2xπ. Calculation: The limit of limx→∞2+x2xπ apply L'Hospital rule.…

Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

A: Explained below

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: 2 2- limx-1 sin(x3-1) x-1

A:

Q: 2-Vx2-5 2. Solve lim x--3 =? (Don't use L'hopital Rule) x+3

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Q: 1 COS X 13. lim- ズ→0 14. lim e -3x+4 15. lim 4x+7 ー-00

A:

Q: 2 lim (cosx)x² =?

A: We have to find the limit

Q: by L'Hopital's rule 1-cos(x) lim x2

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Q: lim 1 5 arctan 4arctan 5 :? Use L'Hospital's Rule 4 X-0

A: wherever an indeterminate form of 0/0 or ∞/∞ exist, we can apply the L'Hospital's Rule. According to…

Q: 2) lim 1-cos (2 arc sinx) In(a+x2) calaulate the limit.

A: Solve the limit limx→01-cos2arcsinx1n1+x2

Q: х —9 Determine lim V6 - Vx-3 x→9 |

A: HERE WEMUST KNOW ABOUT L'HOPITAL RULE

Q: Prove that ) - arctan x + A if x -1 - 4

A: We have to prove: tan-1x-1x+1=tan-1x+3π4   if x<-1tan-1x-π4   if x>-1 Taking LHS, putting…

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

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Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

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Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: Question 5 Transform the function lim x +3-x²) into an equivalent quotients to enable you to apply…

A: Given query is to transform the function to apply L'hopital rule.

Q: 1 lim х-0+ \x = 0 Arctan x,

A: Topic = limits  As per guidelines, At a time only one question can be answered.  please repost for…

Q: Question 5- Evaluate the limit. Vx-1 lim Question 6 - Find the equation of the tangent line to y = -…

A:

Q: 4- Evaluate the limit. for full credit. Sin(-250) limx-0 370

A: Recall: limθ→0sinθθ=0

Q: Question 3 arctan(3x) lim ( Select) X--0 ex -1 1/x lim x--0+ In x ( Select)

A: to find:- limit.

Q: 6x +55 –5 lim X +5 x+ -5

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Q: (2-4* limx-1 sin(x³–1) X. x-1

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Q: solve using L'Hopitals Rule 5. Lim    (1-cos4x) / xsinx   x->0

A: Given limx→01-cos4xxsinx

Q: 1- cos 2x 5. Calculate the limit lim using a) l'Hopital's rule b) vanishing functions x sin 3.x

A: For the solution follow the next steps.

Q: 6.) Use Theorem 4 lim x csc 3x e 7.) Use Theorem 4 lim e -0 sin? e

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Q: 4 - V5t + 1 lim +3 vt +1– 2

A: Let L=limt→34-5t+1t+1-2

Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

A:

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin(2x - 6) sin(4x - 12)…

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

Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: 17. Find limx cos (4) using Squeeze Theorem. x-0

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Q: Evaluate limt-->0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt-->0(sin 3t)/(sin 6t).

Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

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Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: lim- XVx 1 5 arctan 4 arctan 5 ? Use L'Hospital's Rule 4

A:

Q: 1 x |=? Use L'Hospital's Rule 4 lim- 5 arctan -4 arctan 5 xVx

A: