Use l’Hôpital’s Rule to find the limits in Exercises 77–88. x² + 3x – 4 77. lim 78. lim tan x tan x 80. lim x0 x + sin x 79. lim sin? x sin mx 81. lim 82. lim x→0 sin nx x>0 tan(x²) 83. lim sec 7x cos 3x xT/2 84. lim Vx secx x→0+ 85. lim (cscx – cotx) x→0 86. lim x→0 ) 87. lim (Vr + x + 1 – Vx² – x 88. lim x² + 1

Q: Verify that L'Hopital's Rule applies and evaluate the limit.

A: The given question belonging to the calculus in which we have to find the limit of the given…

Q: 5. Informally explain, using the precise definition of a limit terminology, why the limit lim sin…

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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: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: 2) By using E-S definition of limit, show lim (x+y+xy)cos÷ cos 음-0 COS (xy)(0,0)

A: Let f(x)=x+y+xy cos1x cos1y

Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and…

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Q: Evaluate the limit. limx→ 0+ tan-1(1/x)

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Q: Use l’Hôpital’s rule to find the limits in Exercises . x² . 8. lim x--5 x + 5 х — 2 7. lim x→2x2 25…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: 4) Use L'Hosp9tal's Rule to find the limits c) lim tanx)) メ→0 d) lim (ex + メ メ→ o

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Q: 2] Show that the limit does not exist by considering the limits as (x, y) → (0, 0) along the…

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Q: Use L 'Hopital's Rule to find the limit:

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Q: Compute the follow ing limits. ) lim X-2 メ→2 Jx lim sin(x3 X>0

A: NOTE: Refresh your page if you can't see any equations. . multiply and divide by

Q: lim x→0 sin(5x)/4x  (a) using regular techniques  (b) using L'Hôpital's Rule

A: Given, (a) limx→0 sin5x4x  Multiplying and divide by 5 limx→0 sin5x5x *54  1 * 5/4…

Q: 2) For lim (5x)4*, do not evaluate! x→0+ a) Which indeterminant form is the expression? b) Set up…

A: a) The given limit expression  =limx→0+5x4x=00 form

Q: Use calculator graphs to make approximations for each of the limits in Exercises 67–74. 67. lim(3 –…

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

Q: evauluate the limit lim x→0 (sin2 (3x))/ x2

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Q: Use l'Hopital's Rule to evaluate the limit. lim X x→0 sin x O 1 O -1

A: This question is related to the limits, we will solve it using given information.

Q: 2. Find the limit or show that it does not exist: lim (2,y)→(0,0) 2x6 + y?

A: We have to find limit

Q: Calculate the limit limx→π/2(tanx)cosx.

A: We have to evaluate limx→π2tanxcosx We know that tanπ2 is not defined. Therefore, we will simplify…

Q: Use l'Hopital's Rule to evaluate the limit. lim x-0 sin x O 1 O-1

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Q: Use l'Hopital's rule to find the limit. 20 lim x sin- O 1 O 20 O 1/20

A: Explanation and solution is given below....

Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

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Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

Q: Use L 'Hopital's Rule to find the limit:

A: Given limit is Therefore, given limit is of indeterminate form

Q: lim r3/2 sin (1/x)

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Q: 1. Use L'Hopital's Rule to calculate the following limits: (a) lim- sin . (b) lim,1- T/2-sin-la…

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Q: Explain why lim (csc 0 – cot 0) involves an indeterminate form, and - then prove that the limit…

A: limθ→0cscθ-cotθ By applying the limit directly, we get limθ→0cscθ-cotθ=csc0-cot0=∞-∞ Which is an…

Q: Evaluate the limit lim sin (). x-4 lim sin-() = %3D x→4

A: Evaluate the limts

Q: Evoluate the limit of (1-cosx) (x²) as x pproaches 0.

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Q: 5. Informally explain, using the precise definition of a limit terminology, why the limit lim sin…

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Q: Use L 'Hopital's Rule to find the limit:

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Q: Find the limits in Exercises 25–30. sin (1 – cos x) х sin x 25. lim x→0 26. lim x-0" sinVx sin (x² +…

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Q: Use l'Hopital's rule to find the limit 10 lim x sin X-00

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Q: Divide numerator and denominator by the highest power of x in the denominator and proceed from…

A: Hello thank you for the question. As per our guidelines, We’ll answer the first question. Please…

Q: Use the first result to find the limits a. lim sinx = 1 X-0 x i. lim X-0 sinx lim cosx x2 ii. X-0…

A: Given: a limx→0sinxx=1

Q: x²y lim (x,y)→(0,0) x2 + y?

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Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

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Q: Use l'Hopital's Rule to evaluate the following limits: lim (Va – In (x)) lim (1 – æ)'-* x→1+ lim…

A: I am attaching image so that you understand each and every step.

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 0 xsinx(1/x)=0

A: To prove:

Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hôpital's Rule. sin(2x) lim 5x…

A: Limit: a)    x→0limsin (2x)5x=x→0limsin (2x)2x*52=25x→0limsin(2x)(2x)=25.1=25We know ,…

Q: b) By using "L'Hopital rule"; Find the limits of:- (1) lim,o In (sec x) 3x 2) lim,* (tan x)*

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Q: Use L'Hospital's Rule to evaluate the given limit. x+x a. lim X--0 sinx b. x-1+ lim -) In x, c. lim…

A: Let us consider a limit function limx→af(x)g(x) If the limit is of the00 form then L'Hospital rule…

Q: evaluate the limit, do not use lhopital's rule 1-x+2x+7 limx→-x 2 V 9x +5 - 3x

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Q: 1f. Use L'Hopital's Rule to find the Limit: lim (tanx)x x->0+

A: Given,

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: Use L'Hospitaľ's Rule to evaluate the given limit. x²+x a. lim X-0 sinx

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

Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

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Q: 8. Find the limit using squeeze theorm. lim x² sin(x²)

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Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

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