1- s2021 a) lim tan s b) lim - 2² + =-1 lim xA *(x-1) + Gx-1) lim c Ce -1) lim 22 + 15z* – 32x3 – 2021r + 1 17+ 5z4 + -2x3 - c) lim

Q: 1) Find limit 1. lim x-0 tan 3x x3+2x2-3x 2. lim x-3 x3-2x2-15x Vx+1-V2x 3. lim x-1 x2-x 1 4. lim- x…

A: Given

Q: 11. Use L'Hopital's rule to find the following limits. x² + 3x-4 x-1 (a) lim x-1 In x xx-1 (b) lim

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Q: Clearly show why evaluating lim x (In x)2 requires repeated application of L'Hopital's rule. Show…

A: We have to evaluate the limit of the function fx=xlnx2 using the L' Hopital's rule. To find the…

Q: Prove the lim(Sn) = -∞ case.

A: We use the notation uN =inf{ sn :n>N},              vN =sup{ sN : n>N }, u = lim uN = lim inf…

Q: f has domain of (-∞,–1)U(-1,2)U(2,00) lim f(x)=- %3D x→ -1" lim f(x)=- x→ -1* lim f(x)=3 x→2

A:

Q: 2. Evaluate the limit: TC 1000 lim x-7- (x-7)2 lim x→8+ (8 - x)3

A: the given limit is: limx→7-πx-72-limx→8+10008-x3 we have to evaluate the given limit.

Q: 3n Find lim„→∞ (1+)" . Hint: Apply L'Hopital's rule.

A: Please refer the attached image for complete solution.

Q: Which will best solve lim *-6x+9, х-3 x-3 O Derivatives O Limits of a function O Indeterminate forms…

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Q: Use L'Hopital's Rule to evaluate the exact value of lim(x² – 2x+1)*-1.

A:

Q: prove that lim x-->0 x^2 cos 1/x^4 = 0

A: given limit squeeze theorem

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: 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: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

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Q: lim 21/* is no limit 1

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Q: 1 Only one of these calculations is correct to evaluate the limit lim 1 tanhx Select one: O im…

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Q: 4. Use L'Hopital's Rule to find (a). lim 22-In 2 3+2z

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Q: Using e – N description to prove that lim - = 0.

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Q: Extend L'Hopital's Rule to evaluate lim (x2 - x) x-+

A: See the attachment.

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: х —9 Determine lim V6 - Vx-3 x→9 |

A: HERE WEMUST KNOW ABOUT L'HOPITAL RULE

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

A:

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: Use L'Hopital's Rule to evaluate a) lim XXX b) lim X-2 2x e 4x 2x²-5x+2 5x²-7X-6 2

A: Let f(x) and g(x) are two continuously differential function at point 'c'. Then,…

Q: Find f(a)  a=2

A: We know that the definition of derivative is: We write the given equation in this format and find…

Q: Use l'Hopital's Rule to evaluate the limit. x2 - 9x + 20 19) lim X→5 X - 5

A: Consider the limit  limx→5x2−9x+20x−5

Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: 1a. Use L'Hopital's Rule to find the Limit: lim         (xsinx + x2 - 4x2)/x - 2pi x->2pi

A: Let's understand the L’Hospital’s Rule If where a is any real number, infinity or negative…

Q: Prove lim 7-x =6 using the ɛ,8 definition (precise definition) of a limit. x2 2

A: Given data:     The given expression for the limit of the function is: .   The given expression for…

Q: ve that lim 1 by definition.

A:

Q: • Find the limits of 2+x-V2 • lim Vx -3 • lim X→9 x-9 x³+1 lim X--1 x+1 V5+x -V5-x • lim x-0…

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Q: Compute the exist i. lim 8+iz 2--2i z+4 following limies if they . ¡i. Gm Rez.

A:

Q: find the limit of lim x->3 sin(x-3)/x^2-x-6

A: To find limx→3sinx-3x2-x-6

Q: lim cos nл| 2n-1 - 2n+2

A: Use : cos x =1-x22!+x44! + ...........

Q: 2. Use L'Hopitals's rule to find lim (-).

A: Given that: limx→0+1x-1ex-1

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

A:

Q: 5) Prove that the order of iteration of limits can be significant by showing that х2 lim(lim у-0…

A: It is needed to prove that order of iteration of limits can be significant by showing that:

Q: 5- x 37. lim In

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Q: Use l'Hopital's Rule to evaluate the limit. x2 - 6x + 5 16) lim х-5 х -5

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Q: lim x in (It -)

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Q: 91_در lim 2-3 z²+4z-21 LIMIT VALUE: lim 2--1 LIMIT VALUE: lim (x³ +7x² - 2x + 4) 2-2 LIMIT VALUE:…

A: Solved below

Q: Prove that lim (4x² – 25) = -9. X→2

A: We will prove this by definition of limit as follows

Q: 5. Using the appropriate precise definition of limit, prove that limx-→4+ +0o. Show all work. X-4

A: Here, we need to show the limit by the precise definition of limit. We are given that…

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: (a) Find the limit (if exist): lim "(2t-2)2 dt 2x-1

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Q: 5. Determine if the limit exist (hint: use two-path test) (Баллов: 2) lim(zy)-> (0,0) O Not possible…

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Q: State the value of each of the quantites below. A) limx---> -4^-   F(x)= B) limx---> -4   F(x)=…

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Q: (9) Use L'Hopitals Rule. (a) Compute lim (e² + x)-1/x tan(4x) In(x + e*) (G- (b) Compute lim a)…

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Q: Prove lim x ---> 3    (1/3x+1) =2

A: It is known that if we have a function f(x), and limit x tends to a, then the function can be…