QUESTION 1 a) Evaluate the following limits and verify your a 3y +5xy+2x Зу' +2ху (1) lim (-») -в,-2) Зу+2ху 4(x² -y') (i) lim (x.y) (0,0) x² – y² +1-1

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Q: QUESTION 10 Compute the limits. Justify your answer. (You will receive no credit without showing…

A: The limit of given function is computed directly by using some results

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A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

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Q: 3 If lim f(x) = 3.5 and lim,-2+ f(x) = 6.5 the function has a double sided %3D x-2- limit or one…

A: A limit is the value that a function approaches as the input of that function approaches a certain…

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

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Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

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Q: Show limx→∞ xne−x = 0 for all n = 0, 1, 2, . . . . To get started notice that when x ≥ 0, all the…

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

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Q: 5. If lim f(x, y) = 5 (x,y)→(3,–7)" %3D for every curve C in R? containing the point (3, -7), what…

A: If limx,y→3,−7fx,y=5  is true, then it represents that limit exists atpoint (3,-7) for function…

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Q: Question 19 Let f(z) = 3x + 8x 7. According to the definition, f'(x) = lim %3D (Enter the expression…

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Q: 8 - x- x2 if x 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: lim (In w-

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Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

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A: L’Hospital’s Rule: Suppose that  limx→a f(x)g(x)=00  OR  limx→a f(x)g(x)=±∞±∞ where a can be any…

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Q: Choose the limit that would NOT use l'hopital's rule. 1³ – 1 lim I →1 1² – 1 (=* – 1) (=² – 1) * lim…

A: We can find the answer as given below

Q: QUESTION 2 Prove using the definition of a limit that lim x² + y2 -y = 4. >

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Q: Question 5 Transform the function lim x +3-x²) into an equivalent quotients to enable you to apply…

A: Given query is to transform the function to apply L'hopital rule.

Q: sin 0 = 1 to determine the limit. Use the relation lim 0→0

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Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: Question 3 arctan(3x) lim ( Select) X--0 ex -1 1/x lim x--0+ In x ( Select)

A: to find:- limit.

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A: For the solution follow the next steps.

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

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Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

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Q: (x +2x =-6x if xS-2 if x>-2 A) Check the continuity of the function s(x) at x = -2 S(x) = ++ B)…

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Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

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