II. Apply the limit laws on the following: lim x→2 `x3-x 1. 2. lim (Vx/V) X-1 .cos x lim (*)(**+x² 3. X-3 X-1

Q: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

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Q: Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?

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Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: Determine the following limits analytically.

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Q: 6 — х — а? if x 1 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

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Q: Use l'Hôpital's Rule to evaluate the limit. COS X lim -X- 3. 3. O A. -3 V3 O B. C. 2 O D. -/2 1.

A: We have to find limit As per guideline we have to solve one

Q: 9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits: (a) limx→3 2f(x)…

A: Given that limx→3f(x)=2 and limx→3g(x)=-5

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

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Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: - x² if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x…

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Q: Evaluate the following limits (if exist): 1-cos(ax) (c) lim- a+0 (d) lim/Vxr'+x-Vx°-cx), where c is…

A: To evaluate the given limit we are using L- Hospital rule

Q: 2. Use L'Hospital's rule to evaluate the following limit. cosh(3x) – 1 lim x→0 x2

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Q: Use l'Hôpital's Rule to evaluate the limit. cos (3x)-1 lim x² 2.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: 04: - Evaluate the limit of the following: x3–1 lim x→1 4x3-x-3 sin 2x lim 2) x-0 2x²+x 1-V 3) lim…

A: Q.4). (1) To evaluate the limit: limx→1x3-14x3-x-3. Solution: We can find that it is 00 form. So, we…

Q: Use L'Hôpital's Rule to find the limit. 5. lim x0 e2- xr- 1 5 cos x

A: l'Hosptital's rule provides technique to evaluate the limit with indeterminate form.

Q: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x 4/3 X (a) lim x1 x³…

A: According to Bartelby's guidelines we can only solve first three sub-part at a time. Please post…

Q: 1. Find the following limits proving whether they exist or do not exist x² yey lim A) (x,y) →(0,0)…

A: Solve the following

Q: Use l'Hôpital's Rule to evaluate the limit. 2 - 4x+2 lim 2. X>co X+5x+11

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: II. Apply the limit laws on the following: lim (Vx/VA) 2. X+1 cos x x5+ lim X-3 3. X-1

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Q: 1. Prove rigorously that the following limit does not exist lim arctan x-0

A: limx→af(x)≠L: There exists ε>0 such that for every δ>0, there exists x such that…

Q: 5x2 + 10x + 1 20. lim x* + x² + 1

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Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

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Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

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Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

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Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x²–4x lim x→0- |x| (i) (ii) 2tan?x…

A: Part i,Given,           limx→0-x2-4xx

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: (1) Evaluate the indicated limits, if exist (x³ + 1) -x (а) lim r+0 V9 + x² (b) lim In I→1+ (c) lim…

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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: 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: 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: - x – x2 if x 2 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: 2. Find the limit of the following function sin(x - 4) lim- x-0 x- 2

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Q: (a) Compute the following limits: (i) lim **+x²+x+1 x2-1 sec-1(vZ+h)-sec-1/2 (ii) lim h→0 h

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

Q: Find the limit. lim vx+11 cos (x + 3T) X-- 3T lim vx+11 cos (x + 3r) = →-3T Type an exact answer,…

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Q: [ 2 Let f(x) x – x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not…

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Q: 2. Determine the infinite (∞ or -0) limit as follows: x² – 2 - (a) lim x2- x2 3x + 2 - 4-6 sin x – 1…

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→ ∞ x²

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Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Evalvate the limit lim Cos x In(x- TT Xーつク nピ-e)

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Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x² –4x lim x→0- ]x| (i) 2tan?x lim…

A: (1). From the given problem: limx→0-x2-4xx

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

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Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

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Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

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Q: Find the limit. lim Cn (3+x)- In (l+x)]

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