b) Evaluate the following limits. (Answer three only) sin(2x) cos? x - sin(2x) cos x x*- бх - 16 Vx + 15 -5 ,2) lim x+2 x-64x tan (3x) 4) lim- -o sin(10x) 1) lim 2x(1 — сos x) 3) lim 1-10 х— 10

Q: Compute the following limits if they exist. sec r – 1 (a) lim z-40- 23 I – sin r (b) lim 1+0 x - tan…

A: L. Hospital RuleIf limx→a f(x)g(x) = 00 or v6c6 formThen differentiate f(x) & g(x) and take…

Q: b. Evaluate the following limits: 7x cos)-7x lim- [sin(-2x)sin(5x)sin(7x)] lim 5x2 2x cos(x) X-0

A: We write the given limit in the following format

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: 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: #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: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

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Q: (z+2 z< 0 sin (x) 0<æ Let F (x) = Then lim F (x) =

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Q: Suppose the inequality (x² – 4x + 3) < f (x) < cos ( TX *) holds for all values of x. 2 Find lim f(…

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Q: 1. Determine whether or not each of the following limits exists as a real number or as +oo or -oo.…

A: According to the given information it is needed to check whether the limit of the following…

Q: (g) Find the value of a and b such that the following limit exists. if x 2. a cos x + 1 sin(5r) x2…

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Q: 1. Evaluate the ff. limits: -1 (e*). V1 – e2¤ sin' 2 lim (а) x→0- - 1 - (b) lim x + sin

A: Explanation of the answer is as follows

Q: 1. a. Evaluate the following limits and find the value of K from the given equation: lim( x→1 Nx5-N…

A: Here we need to find Limit by using L'hospital rule.

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: 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: We can use direct substitution in computing limits provided there is nodivision by zero, which is…

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Q: q//// find the limit of the following: 1- lim x* cos n-0 2- lim vx? + x³ sin n--0

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Q: 1. Solve the following limits. (a) lim II 1+ r? x In x (b) lim 2+ sec (3x) (c) lim /6 tan (3r)- 1

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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: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

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Q: In evaluating 2 2 dx XV is same as evaluating lim_ cos-¹(f(x)). Determine the value of f(x) if x=2.9…

A: As per the question we are given a definite integral and we have to find the primitive of the…

Q: Show that Hint: Use to obtain In[|x|] √√2/T. 1 - cos(sx) x² 8 1 - cos" x x² lim n-√√n 00 2 π dx |s|…

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Q: B. Compute the limits of the following trigonometric functions. sin 1.) lim x+2 2.) lim X-0 Cosx x-0

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Q: Evaluate the following limit. 3t cos t+ - 1 e - 3t - 1 i- sin t lim j+ 5t 6t sin t 3t e - 3t- 1 cos…

A: NOTE: Refresh your page if you can't see any equations. .

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: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

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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 limits: Vx + 25 – 5 (а) lim т? + 5х + 1 (b) lim x→2 x3 – x – 1 1– sin 0 (c) lim 05 1+…

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Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: 2. Evaluate the following limit. 1/x lim (1– sin 3x)"* x→0*

A: Given, limx→0+1-sin3x1x    We have to evaluate this limit

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: 5. Evaluate the following limits: sin(6x) а. lim x→0 5x3-4x cos e – 1 b. lim sin 0

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Q: 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…

A: Hey, since there are multiple questions posted, we will answer first three question. If you want any…

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

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Q: 2. The limit of the following function equals: x2/3 + x-1 lim x--00 x2/3 + cos2 x

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Q: 1. Evaluate the following limits: (i) 4 sin(r + 4) lim 4 sin 8(r+ 4) (ii) 5 sin(6z) lim 0 sin(5x)…

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Q: b): Evaluate each of the following limits: 1- cos* 3x 1)lim 9x2 x sin 5 12)lim r+00 xt + 1

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Q: 10. Evaluate the following limits. e* +e* – 2 lim 1- cos 2x b) lim x² Inx a)

A: see below the answer  and calculation

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

A: Solution:-

Q: 4) dr In((3x² – 4x + 7)(5x³ – 9x)®) Hint: applying properties of limits will help you avoid using p…

A: Given, 4) dln3x2-4x+75x3-9x8dx  5) dcos4x2-5dx  We have to differentiate it.

Q: B) Evaluate two of the following limits 2) lim(cos² x – sin² x) - 8

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Q: 1. Find the following limits proving whether they exist or do not exist y² sin x X E) F) lim (x, y)…

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Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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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: q//// find the limit of the following: 1- lim x* cos 2 n→0 2- lim Vx2 + x3 sin-

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Q: 1. Compute and completely justify (by citing the appropriate results and theorems) the following…

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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: In evaluating 4 2 dx X√ X²-4 is same as evaluating lim cos ¹(f(x)). Determine the value of f(x) if…

A: We have to find the value of f(x).

Q: Evaluate the limit. 1- r + In (x) lim I+1 1+ cos (3 7 x)

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Q: 16) [5] Compute the value of the following limits using L'Hôpital's Rule: Ax -1-4x a) lim x40…

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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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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.