Which one is correct, and which one is wrong? Give reasons for your answers. x? – 2x 2х - 2 lim a. lim x>0 2x – cos x sin x 2 = lim; x02 + sin x 2 1 2 + 0 x? - 2x 2x – 2 -2 b. lim x→0x² – sin x = 2 lim X→02r cos x

Q: Cos x-1 2- Show that lim = 0

A: We have to find the limit of the given expression. this can be done as follows:

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Q: x²+1 lim tan (x,y) → (0,1) x? +(y-1)². O is equal to 0. O is equal to -II

A: Given that: lim(x, y)→(0, 1)tan-1x2+1x2+(y-1)2

Q: Q3/ Solve the following. Choose two only. 1. lim x lnx³ X-0 2. lim x sin(1/x) 818 ex+2x 3. lim 818…

A: According to the question, we will calculate the limits of any two subparts.

Q: 1. x² tan( + 47) + 2 tan-1x lim =? (a) 1 (b) -2 (c) -1 (d) (e)

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Q: 2. It can be shown that the inequalities x2 x sin x < 1 1 2 – 2 cos x hold for all values of x close…

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Q: 1- cos 5x lim x? 2 x→0 а. -2.5 b. -12.5 С. 12.5 d. 2.5

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Q: b) Evaluate the following limits. (Answer three only) sin(2x) cos? x - sin(2x) cos x x*- бх - 16 Vx…

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

Q: A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this…

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Q: Which of the following may be solved by a direct application of L'Hopital's rule? sin 2x lim x→0-…

A: We have to check

Q: solve

A: Note: Since you have to ask multiple question, we will solve the first question for you. If you want…

Q: ENGG MATH 2 1. lim- X--0 x2 1-cosx 2 sec?x-2tanx 2. lim X-n/4 1+cos4x Vx² +3 3. lim X-00 x 4. lim…

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

Q: Ix2 The inequality 1- sin x <1 holds when x is measured in radians and x<1. sin x Find lim if it…

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Q: x? 16. lim 0 1- cos x 1+ cos 0 18. lim 0 1- cos 0 x + x? 20. lim x- 1- 2x²

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Q: 44. lim sin² x x→n/4

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Q: In evaluating 4 2 2 dx x√√x²-4' is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: x* –1 lim 6 sin x For B = - which one is B? x→0+

A: We have to use series expansion here.

Q: find the limit or explain why it does not exist.

A: Question (1) - Let the limit be y - y = limx→0 x2-4x+4x3+5x2-14xy = limx→0 x-22xx2+5x-14y = limx→0…

Q: tan( xy) lim (х.у) >(0.1) х"у+x = ? 1 (b) 2 1 (c) 3 (a) 0 (e) 1

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Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: et - e* lim,0 2 sin x

A: Consider the given function, limx→0ex-e-x2sinx put the value of limit into the function,…

Q: how do I solve this problem ?lim x-0 1-cosx/cos^2x-3cosx+2

A: First we use substitution property of limit, and that's given an undetermined form.Then we use…

Q: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

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Q: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

Q: 8 sin (1r) 3. Find lim 5.r

A: In the question we have to find lim x→08sin(4x)5x

Q: x²+3x (t – 1)e' dt 2л — 4 - lim x→2

A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: x* +x? 5. lim, +* e* +1 In x 6. lim, csc(6x) csc(2x) 7. lim 5x+ 2lnx 8. lim, X+3lnx 2Tan 'x-x 9.…

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Q: 2 dx 5, is same as evaluating lim cos C+2+ F(<x))". Determine the value of f(x) if x=3.22 In…

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Q: tan(xy) = ? lim .2. (х.у) >(0,1) х*у+x 1 1 (b) 1 (e) (d) - (а) 0 (e) 1 4 - |3

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Q: 2cos?x – 1 lim tan(2x) sin 5x lim x→0 lim х-о бxsec(3х) x2 + sin 2x lim cos x – sinx 8x 10x

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Q: Q2: Evaluate: [1] 21 lim m COSXVI+ COSX – v1-x, sin-1(x) V1+x - [3] lim-o

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Which one is correct, and which one is wrong? Give reasons for your answers. x? – 2x 2r – 2 a. lim…

A: Limit: a.    x→0limx2-2xx2-sinx         [≡00form]=x→0lim2x-22x-cosx=-2-1=2So a. ans is wrong.

Q: Evaluate lim sin(a+2x)-2 sin(a+x)+sin a x2

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Q: 1 1 X sin x+sin 2x Q3/ Find the value of (x) if5 -2 1= lim 3x -1 1

A: See the attachment

Q: Evaluate lim?→0  (1/sin² x)-((sin x)/(x³))

A: Solution: Consider the given limit function is limx→01sin2x-sinxx3 Using the property of the limit…

Q: mor lo1 tan x 47. lim 7/4 sin xr-cos x

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

A: Solution:-

Q: 1 -is 2 + sin x The value of lim a) 1 1 b) c) 0 d)

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

Q: 14.6.9. Show that lim sin(a? + y²) dA(x, y) = |æ|,]y|<n I sin(a? + y?) dA(x, y) = 0. lim %3D…

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Q: lim (sin? x)tanx xn/2

A: We will find the limit.

Q: 1 lim x-0 sin?x x2

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Q: tanx-1 x-n/4 sinx - cosx is the same as The value of lim none of the given choices lim m/4 sinx+…

A: Limit

Q: 8. im e* 2x 9. lim e* 10. lim e* x+00 x00 sin 6x 11. lim 5*+6 12. lim

A: As per guidelines we can solve only one question at a time so if you need more answer kindly repost…

Q: 9) If y = sin(sinæ), then y' is: x + 2| lim (x +3) I→-2- x + 2

A: See the attachment

Q: Which of the following can we solve by using L'Hospital's rule in its given form? x2 lim x--0 eX…

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Q: x2/3 +x-1 lim x-00 x2/3 + cos? x

A: It is limit problem in which we can find the answer by applying given limit in the function.

Q: 2. It can be shown that the inequalities x sin x 2 - 2 cos x hold for all values of x close to zero.…

A: