Compute Lim メーフ4 7x+5 -3 Sin ? X 2)x-70 3X イメ2+2 3) -00 X-7-00 2x-1

Q: 4) evaluate lim x-->2 (2x2 - x - 6) / (x2 - x - 2)

A: Explanation of the solution is given below...

Q: 2. Construct a table of values to investigate 1 if x -1

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Q: Show that lim(5x+2)=-18 x-> -4

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Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

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Q: 2 4. lim x-3+ \3-x 4 9-x2,

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Q: Suppose lim, =1. Prove that lim -(-1)* = %3D

A: Given: limn→∞ an=1To prove: limn→∞ 1n ∑k=1n -1k a2k=0

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

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Q: If (x, y)lim(2, 3) f(x, y) = 4, can you conclude anything about f(2, 3)? Explain.

A: Assume the function z = f(x,y).First observe the value of the limit for x followed by y.

Q: sec x lim sec(3x)

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Q: Evaluate the limit: lim 2x2 cos(3x) 2

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Q: Evaluate the limit: lim 7x2 cos(2x) - 7

A: we have to evaluate , limx→-π77x2cos(2x)

Q: Use the results of Section 2.2 to evaluate lim (5x – 3 0.2545454545 x-3 11 symbolic formatting help

A: To evaluate the given limit.

Q: Compute the limits that exist. lim x---5, 2x - 10/x2 - 25

A: Given: Compute the limits that exist. limx→5 2x-10x2-25

Q: (a) n+ (-1) 2n lim

A: limn→∞-1nn+12n

Q: Using the important lemmas from Sec 3.3, compute 2 tan(-6x) lim 3x

A: From the given problem:   limx→02tan-6x3x   So, limx→02tan-6x3x=-4limx→0tan6x-6x

Q: Find the Limit (sin3x)/(5x^3-4x)

A: Obtain the limit value as follows.

Q: Evaluate using substitution.

A: The given expression is limx→π4tan3x

Q: Show that 2n lim n+2 = 2,

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Q: Compute the limits that exist. lim x---3 2x2 + 16

A: Given: limx→32x2+16 Substitute 3 for x and determine the limit limx→3(2x2+16)=2(3)2+16

Q: Show that

A: Here we have to show that;  limx→-∞1x

Q: (In x)² lim

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Q: The value of lim (trorozac) 2 (1² 1px (ozoz-ozoz) 6202 (17073— 170741) 7 is equal to

A: The property of exponents is anam=an-m. The property of exponents when the exponents are in…

Q: Evaluate using substitution.

A: limx→-π23sin x

Q: Find the limit by rewriting the fraction first. ху - Зу - 7x+21 lim x-3 (х.у) --(3,6) X+3 ху - Зу -…

A: Factories the numerator and cancel out common term than put the limit.

Q: Determine |7x + 42|| lim x + 6 x - -6 + |7x + 42 | lim x + 6 X- -6 -

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Q: Show that 2 x² - y² - 1 lim (x,y) →(1,0) 1 − x + (2y)² - does not exist.

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Q: Evaluate lim f1x2 and lim f1x2 using the figure. xS-00 yA y 5 f(x) 210 10 23+

A: Consider the given graph as

Q: Prove that 2 +22- -6 lim 3, tan x-3tan x lim cos(x+7/6) V2* - 2-

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Q: Evaluate using Theorem 2 as necessary.

A: We have to evaluate: limx→0tan xx We know that limθ→0sin θθ=1 therefore, limx→0tan xx=1 Hence, value…

Q: -Show that lim xsin

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Q: Prove that lim -- (x + 1)

A: we have to prove that: limx→-1-5x+13=-∞   L.H.S:…

Q: nd lim delta -> -4, tan(delta + 4) /5delta+20

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Q: Which of the given limits would result to 3/4.* csc (3x) lim x0 csc(4x) sin (4x) lim 0 sin(3x)…

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Q: Compute limit as x goes to infinity of (4x^3 +6x-2)/(3x^3 -2x^2+x+1)

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Q: Find the limit. 28x-7x lim x4 x→4 2-x 2. 28x- 7x lim 日 x→4 2- Vx (Type an integer or a simplified…

A: The solution are next step..

Q: Compute lim 0 tan-(5x) 5 25 undefined 1 25

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Q: Compute lim tan x→3+ -1 х2-9

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Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

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Q: 4] Show that lim sin( does not exist.

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Q: : Evaluate 1- lim sırix

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Evaluate: lim-0 (cos 2x) 2²

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Q: evaluate using Theorem 2 as necessary.

A: We write tanx using sinx and cosx

Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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Q: Evaluate using substitution. lim tan(3x) x→ π/4

A: Given: limx→π4 tan 3x To evaluate: The value of the limit.

Q: Find the Limit lim cos(12x-cos(3x)) x->7pie/6

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Q: Find the limit. 4et – 4 1 + t – 1 2 - - lim 1 + t,

A: When limit is of the form 00 or ∞∞, then L'Hospital rule is used. In this rule,take the derivative…

Q: Evaluate: lim       (1-cos-1x)csch(1-x) x→1-1

A: To evaluate: limx→1-11-cos-1xcsch(1-x)