Determine the indeterminate forms of the following and solve them using L'hopitals rule. a. lim -1-x x→0 x2 b. lim V1+2x-vī-4x e2t -1 c. lim x→0 sin t

Q: Match the values on the top with the given limit. A -o BO C 8/9 D +co 9 x2+12 x +9 lim 64 - x2 X- 8-…

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Q: evaluate using Theorem 2 as necessary.

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Q: Find the limit infimum and limit supremum of the following x₂ = Yn where Yn is bounded. Хр n lim…

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Q: use the > & delinit of the f unchions ho prove that i Lim J19-X 3

A: The epsilon-delta definition of the limit: Let f(x) be defined for all x≠a over an open interval…

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

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Q: 1) Find the following limits. Do not apply L'Hospital's rule. x² +x – 6 lim 142 r2 - 2r (a) sin(1 –…

A: 1) a) From the given problem:   limx→2x2+x-6x2-2x   Simply we can write as:…

Q: 1. Compute the following limits analytically. -24.x +11x +21 а. lim 6x – 7x+12 b. lim (2x²…

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Q: et+ e-X-x2-2 d. lim- x→0 sin²x-x

A: Since there is the symbol of limit, hence limit of the function helps to find the answer to the…

Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

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Q: Q1) A- Prove that: cotx = - tan-1x B- Find: 1. lịm 2. lim(v9x2 - x- 3x) cotx

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Q: 1. Solve the following limits. (a) lim 1-- V1+ r2 x Inr (b) lim 2-0 I+ In r 2 + sec (3r) (c) lim…

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Q: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

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Q: 1.Evaluate each of the following limits. Be sure to indicate if and when you apply LHopital's Rule."…

A: 1). a). To evaluate the limit: limx→0lnx+1e2x-1 Solution: It is 00form. When it is 00 or ∞∞ form…

Q: 3.lim X→π In(cos2x) (π - x)²

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Q: (a) ' Compute the following limits 7x3-5x+1 (i). limr→0 4p3+a²+x-8* (ii). lim,0 V5x+1–1 5x (iii).…

A: a) limx→∞7x3-5x+19x3+x2+x-8= limx→∞x37-5x2+1x3x34+1x+1x2-8x3limx→∞7-5x2+1x34+1x+1x2-8x3=…

Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: Q2: A. Evaluate each of the following limits without using “L’Hôpital’s Rule": (1) limx→0°…

A: 1) limx→0sin(cos(x)-1)x22) limx→-∞5-x3-4x22x3+x2-8

Q: Let y(t) be a solution of ý = y(1 - ;) such that y(0) = 4. Determine lim y(t) without finding y(t)…

A: Given that y(t) is the solution of y.=12y(1-y2)with y(0)=4To find the limitlimt→∞y(t)

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

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Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

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: [4] (a) Show that lim (xa)-(0,0) 2x+y? y-mx, or along any parabola y= exists and it's approaches to…

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Q: sec lim x→1+ Vx7-1

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Q: Prove, using the formal definition, that lim→-1 (T+1)² +0o. %3D

A: We have to find the limit limx→-13x+12=+∞.

Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

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Q: Q3: Find the following limits if exist:- 1-cos 2x (1) limx-0 sin² x

A: If it is required to evaluate the limit limx→af(x)g(x)=00. That is if applying the limit leads to…

Q: Compute the following limits if they exist. 2 - VE (a) lim 244 3 - V2x + 1 (b) lim r sin

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Q: Solve the following expressiol Vx2 + 3 lim x→1 x² – 1

A: Here we have to solve,

Q: Q2/ Find the following limits: 3- 5/27+81 x--00 2/12+Vt²-167 A. lim 1 В. lim-1 x+1 1-sin t С. lim #…

A: We have to find the limit of the following... A. limx→-∞t13-5t2+81142t2+t23-1612B.…

Q: Calculate the following limit: lim(1x)4 sin(13a x→0

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Prove that lim vx sin (2) = 0 using the Squeeze Theorem. x-0+

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Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Please I want solution of sub-parts question 5 with step by step. Many Thanks

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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Q: Could you use L'Hopital's rule to solve the following question in its current form: lim,0+ In(x+1) O…

A: We have one of the following form limx→af(x)g(x)=00 or  limx→af(x)g(x)=±∞±∞  In these cases we have…

Q: X-0+ lim (sinx)tanx X0+ 4.

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Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: - Find the limits using L-Hopital's Rule: cos 3x 1 (а). im $ x→0 X* (b). lim (e - 1)*

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Q: Is In(x² – 1) - 1) 6. Evalaute lim n cos(x)-1 r lulx2-1) lem lulx²-1)

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

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Q: 2. Use the given values to set up a table to evaluate the limits. Round your solutions to sin 3x…

A: limx→0sin3xx

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Which of the following limits does not yield an indeterminate form? a.limx→0 3x^2/x−sinx b.limx→2…

A: (a)lim(x→0) (3x2)(x-sin⁡x)=00form(indeterminant form)(b)lim(x→2) lnx2(x2-5x+6)=00form…

Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

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Q: 6. lim (sinx)* X0+

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