B. Evaluate the following limits. 1+x-e* 2. lim x-0 1-cos x Csc t 4. lim (cos t)ª t→0 csc e

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

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1. Determine if the following limits exist: 1² + y? (a) lim (1,y)→(0,0) e² +y² – 1 12 sin(y) (b) lim…

A: In the question we have to find limit.

Q: Determine if the following limits exist: x² + y5 lim (x,y) →(0,0) 1 - cos(x) + y² (a)

A:

Q: #1. Write the following limits as definite integrals. lim E"[2(ck)² – c]Ax а. 'k = 1 ||P||→0 b. lim…

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Q: Find the following limits, using L'Hospital's Rule where appropriate. cos(mx)- cos(nx) (a) lim x-0

A: The objective of the question is find the limit.

Q: Find the limit: lim (e-3t i+ t2 j+ cos 2t k sin?t

A: Limt-0(e-3ti + t2j/Sin2t + Cos2t k).

Q: Which of the following limits has a value 0? In x I. lim II. lim X-0 e* Neither I nor II. O l only…

A:

Q: 8. Which of the following limits is equal to x* dx? (A) lim E 3+ n) n k2 (B) lim 3+ n) n k=1 2k* 1…

A: Explained below

Q: evaluate the limit. lim e2 'i+ In(t + 1)j + 4k

A:

Q: Determine the following limits analytically.

A: Given, limx→π3sinπ3-x2cosx -1

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

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Q: Evaluate the following limits. lim(Vx? +4x+1-x) a. lim tan (1/x) 1oitonh b. c. lim x cos x->0+ 2

A:

Q: 1. Evaluate the following limits. - 2 lim a.+2 -4 V2 +1-2 lim b. i+2 t-2 | sin 7r lim c.0 sin 3r

A: As per as our guideline i am supposed to solve only 3 part of question 1 . And f getting solution of…

Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit

Q: Find the limits

A:

Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: 1. Determine the following limits, or clearly explain why they do not exist. 3 - t+ sint (a) lim L…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Find the value of the following limits: 5y 1-limy→0 tan 10y

A:

Q: to evaluate the limit. 3 1 v 78. lim x→ x Jo im In(1 + e') di | In(1 + e') dt 2

A: Answer is  1/2 Explanation is given below

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

Q: Evaluate the limit: 1-Cos(9h) lim h h >0

A: Find the limit When we plug in 0 for h, the denominator becomes 0 So it is undefined.

Q: 3t-2 sin t+(e-1) lim +1

A: limt→13t-2sint+et-1t

Q: Which of the following limits is equal to x* dx? (A) lim k 1 3+ n00 k=1 n k* 2 (B) lim E 3+ n n n00…

A:

Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

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Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

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Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

A:

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

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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: 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: (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: 1. In each of the following cases, evaluate the given limit. x2 +5x 14 lim エー→2 - (a) x2 - 2x t - 1…

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Q: Compute each of the following limits, or show that the limit does not exist. xY (b) lim (x,y)→(0,0)…

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Q: b) Evaluate the following limits. In(cos r) i) lim 1 ii) lim I+-0 Vr2 + 16+x 1 In x iii) lim х — 1

A:

Q: Given that f(x) = e ,which of the following is equal to the limit F(; + h) – f(}). lim h→0 ? h Oe…

A: From definition of derivative we know for a function f(x),  limh→0f(a+h)-f(a)h=f'(a)

Q: Which of the following limits requires L'Hopitaľs Rule to evaluate? O A. x-2 lim 2x -2 O B. lim e…

A: According to L'Hospital Rule

Q: t 1. lim t40 sin t t 2. lim t40 et - 1 sin(2t) 3. lim 2t t40

A:

Q: Evaluate the limit T: x lim cos 4 x+11

A:

Q: x² + x 1. lim x++∞ e²x + Inx 2. lim (sech 2x) esch x² +0+x

A:

Q: Find the limit. e-4t i + lim t→0 j+ tan(5t) k sin?(t)

A:

Q: 5. Evaluate the following limits: eh-1 a. limp→o 2h а. b. limx→1 1. x2-1 1 c. lim,»∞x tan d. lim,→1…

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

Q: Evaluate the limit lim sin(T cos x) 1 C T A,

A: we need to calculate Limx→π sin(πcos(x))Now we will substitute x = π to get answer .

Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x>1 We have to calculate,  a) limx→1-f(x)=?b)…

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

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

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

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: Find the value of the given limit. lim tan(4x) I I-0 O a) 1/12 Ob) undefined Oco d) 4

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Q: 1. Find the following limit, if it exists. lim (z.1)-(0.0) V2 + y? +1-1

A:

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

A: