A. Evaluate the following limits by constructing their respective tables of values. 1-cos(3t) 1. lim 3t sin t 1-cos t 2. lim 1-cos t 3. lim E0 sint

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: 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: Calculate the following limits. If the limit is co or –co clearly indicate this. Otherwise, for…

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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: 4t2+3t sin t 2. lim t 0 t2

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Q: 1- cos(3t) lim COS 3t

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Q: Choose the correct answer for the following limit S sin t3 dt lim 3x4 (A) (8) -1 (C) 1 4 (D) 4. (E)…

A: Let us consider the function F(x)=∫a(x)b(x) g(t) dt Then the derivative of the function is given by…

Q: (iv) Evaluate each of the following limits without using L'Hôpital's Rule. tant (a) lim t+ sin t

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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: 3. Find the following limits (a) sin(4x) lim 140 sin(7x) (b) cos(30) – 1 lim 0→0 sin(70) (c) sin? t…

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Q: sint 1 COs t 13. lim t+0 t t

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Q: Evaluate the following limits by constructing the table of values. 1. lim 3" 5. lim tan r 0 2. lim…

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

Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: Use l hospital rule for finding the limit.

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: ind the following limits using I sin(Tx) lim -0 tan(ex)'

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Q: 1. Evaluate each of the following limits: sin q-sin a c. lim q-a

A: We apply L- hospital rules.

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: 5. lim sin TT (sin- 3. x→0 2

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Q: 1. Use the definitions of the hyperbolic function to find each of the following limits. sinh(x) lim…

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Q: 1-cos r-r² 1) lim,-0

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

Q: Choose the correct answer for the following limit S sin t3 dt lim 2 x4 (A) (B) (C) 1 8. (D) 4 (E) -4…

A: Given,

Q: Choose the correct answer for the following limit So sin t3 dt lim 2 x4 (A) (B) (C) 8. (D) (E) (F)

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Q: (iv) Evaluate each of the following limits without using L'Hôpital's Rule. tant (a) lim t0 t + sin t…

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Q: csc t lim (cos t) t-0

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Q: find the following limits a/lim cos(0)-1 Os0 sin(e)

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Q: Find each of the following limits. sin x + tan x 1. lim 1- cos?x 2. lim x2 e2x + x ex +1 3. lim X00

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: 1-cos 7y 16. lim y→0 2y

A: Given: limy→0 1-cos(7y)2y We have to evaluate the given limit

Q: I. Evaluate the following limits by constructing the table of values. 5. lim tanr 1. lim 3" 2. lim…

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Q: 1. 14. lim COS sin t

A: Given: limt→0 1-cos(t)sin(t)

Q: Use L'Hôpital's Rule to evaluate the following limits a. Find the limit as x approaches 7 of (x –…

A: We have to find the limits of the given functions as x approaches to the given value.

Q: The value of the following limit Lim (cos(x))ou(x) IS:

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Q: cos(ry) – 1 1. lim(7,9)→(0,0) no existe. sin(2æ) – 2x + y 2. lim(z,y)¬(0,0) no existe.

A: 1 - limit exist

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

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Q: L Evaluate the following limits by constructing the table of values. 1. lim 3 5. lim tan z 2. lim 5…

A: Solution...

Q: - Using any results from the course material, find the following limits: sin(x? – 9) а. lim x-3 (x2…

A: Solution:-

Q: Find constants a and b so that each of the following limits is true.

A: Given: limx→0a+bx-1x=2limx→1tanax-a+b-2x-1=3

Q: Evaluate the following limit. cos t+ 5 sin 2t, et - 3t- 1 lim -1 2 -k -j+ 2t 31? 5 sin 2t lim est -…

A: Use expansion of series then apply limit

Q: csc? x-2 lim lin cot x-1 4 2 lim (x sin) X→+0 lim sec x 2

A: Let us consider the limit of the function limx→af(x)g(x) If the limit is of 00 form then  Apply…

Q: Evaluate the following limits by constructing the table of values. 1. lim 3" 2. lim 5" 4. lim cosr…

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Q: C. Evaluate the following Trigonometric Limits: 1. lim cos 5x TO

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Q: Use L'Hospital to determine the following limit (where t is regarded as a constant): cos(wt) –…

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Q: b): Evaluate each of the following limits: x5 sin? 2)lim x+00 x* + 1

A: Given,

Q: Evaluate the limits for each of the following; sin 3t lim 0 t(t +9) (a) sin? t lim t→0 3t2 (b) (x+1)…

A: limx→0sinxx =1 As you have asked multiple question we will answer only the first three subparts for…

Q: 1+x-e* 1-cos x lim x-0

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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: 1) Evaluate the following limits. cos r - x4 - 1 sin? 2x 3* + cos r a) lim b) lim -00 3+2 – 2* c)…

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Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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Q: - Evaluate the following limit 2 sin z – sin 2r a. lim

A: Evaluate the limit limx→02sinx-sin2xx3