Evaluate the following limits. 2 sin 5x a. lim x→0 3x b. lim sin 5x cot 3x x→0 d. lim (sec x – tan x) x→7/2 c. lim x csc2 V2x x→0 sin x? f. lim x0 x sin x x – sin x e. lim x0 X – tan x x – 8 sec x h. lim x→2 x? g. lim x2

Q: Evaluate the following limits by constructing the table of values. 1-cos(3t) 1. lim- t-0 3t f(). 1-…

A: 2. As you have asked for the solution of question 2 only, so I am solving that. Thank you. A…

Q: Evaluate the following limits using L'Hôpital's rule   2. lim x→0+ tanh x/sechx − 1

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Q: Evaluate the following limits: (a) limx→0 4x/sin 5x (b) limx→π sin( π/2)/5x (c) limx→0…

A: a) limx→04xsin(5x)=45 b) limx→πsinπ25x =sinπ2limx→π15x                    = 015π limx→πsinπ25x = 0…

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: Find each of the following limits. sin x + tan x 1. lim 1 - cos?x x2 2. lim x-0 e2x + X 3. lim ex +…

A: Since you have posted multiple questions and need answer for two questions but we can answer one…

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

A: A) Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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: (b) Find the following limits. Do not apply L'Hospital's rule. x2-4 lim x+2 x-2 (i) sin (31) (ii)…

A: Explained below

Q: sec x -tan x lim -X 2 X- 2 .2 x²+sin 3x lim X→0 2x+tan 2x

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: X COS X - sin Xx sin

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: Use l'Hôpital's Rule to find the following limit. sin (x) – x lim 5x° 3 sin (x) – x lim (Type an…

A: The given limit of the function is, limx→0sinx-x5x3. The L'Hospital's Rule is used when the value of…

Q: Compute the following limits if they exist. tan x x – sin x (а) lim 0+ Vx (b) lim (c) lim tan x- seC…

A: We have to find the limit

Q: How to evaluate the attached limit.

A: The given limit is,

Q: (a) By using L’Hôpital's rule, evaluate each of the following limits. sin x lim x-0 2x (i) (ii) lim…

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

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…

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Q: In which limits below can we use L'Hôpital's Rule? O lim 2x? + 7x + 6 lim x2 + 8x – 9 sin x O lim…

A: L'Hopital rule is used for indeterminate forms.

Q: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

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Q: Q3. Compute the following limits if they exist. sec a - 1 (a) lim x – sin r (b) lim 20 x - tan r 2 –…

A: Q.3 part a) Substituting the limit in function, This is indeterminate form 0/0,

Q: Evaluate the following limits using L'Hôpital's rule 1. lim x→0 e^x(cschx)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

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: Evaluate the following limits: 1/x lim tan +x x→0 4 sinx )/x lim x→0

A: Recall: L' Hospital Rule : suppose that we have one of the following cases, limx→af(x)g(x)=00 or…

Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

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

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Q: Evaluate the following limits. sin- (e") 1. lim 2 V1- e20 1 1 x + sin 2. lim

A: On solving this we will get

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

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Q: lim sin?(2 – x) cot²(x² – x – 2) - X→2

A: We have to evaluate the limit at x= 2.

Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: Compute the following limits if they exist. sec x – 1 (a) lim x – sin x (b) lim x→0 x – tan x 2 - VI…

A:

Q: (c) Find the following limit: Vx +1- 2 lim X-3 x(x - 3) V9x2 + 5 lim x-00 X- 1 cot 0 csc lim sin e

A: Given we have to find the limit

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: Q3: Evaluate the following limits : (solve 4 only) x + Sinx 1+ Sinx a) lim x→ 2x + 5 b) lim x.Sinx…

A: Hey, Since you have posted multiple questions, asper our guidelines we will answer first question…

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: Using l'Hôpital's Rule, find the following limit: 5 - 5 cos x lim x-0 ex – x - 1

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: Compute the following limits if they exist. sec x – 1 (а) lim x – sin x (b) lim I-0 x – tan r

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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: 1. Evaluate the following limits: x2 V2x2 + 1 Vx2 + 5 (a) (3 marks) lim (b) (4 marks) lim a→3 2* +…

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Q: (a) lim θ→0 θ tan(θ) (b) limx→π sin(x) x − π (c) lim t→0 sin2 (5t) t 2

A: Given that : a) limθ→0 θ tan (θ) b) limx→π sin (x ) . ( x - π) c ) limt→0 sin2 (5t) . t2

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

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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: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim +2 x– 2| (1) (ii) sin²(3r) lim…

A: According to question given:(i) limx→2x2-4x-2When x approaches 2 from right x-2=x-2When x approaches…

Q: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

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

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Q: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim x+2 |x – 2| (i) (ii) sin (3t) lim…

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Q: Please show step-by-step solution

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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…