45. a) Find lim h(x). b) Find h(1). c) Is h continuous at x = 1? Why or why not? d) Find lim, h(x). e) Find h(-2). ) Is h continuous at x = -2? Why or why not?

Q: use l’Hôpital’s Rule to evaluate the limit

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Q: 3. Explain why the following limits do not exist. 1 (a) lim x-5 (x-5)2 -x² +3, (b) lim h(x), where…

A: (a) limx→51(x-5)2 Let  f(x)=1(x-5)2 As x approaches 5, (x-5)2 approaches 0, and so f(x) approaches…

Q: b) Now, follow an algebraic approach to compute the limit 13 – 1 lim 1 I-1 and the limit V9+x– 3 lim

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Q: Evaluate the limit.

A: It is given that, limh→π21-cos3hh   It is known, that if we have limx→af(x)g(x) and after plugging…

Q: For a function f, suppose lim f(x) does not exist because the left – hand and right – hand limit…

A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

Q: (a) By using the definition of limit, prove that lim (3x+i z31

A: Introduction: Limits in mathematics are distinct real numbers. Consider a real-valued function "f"…

Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: 3. Use the epsilon - delta definition to prove that the limit is lim Vx x-0 371 when

A: To use epsilon delta definition to show that the below limit is 0. limx→0x3=0

Q: find the limit or explain why it does not exist. lim In (t – 3)

A: limt->3+ln(t-3)

Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

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: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈>0…

Q: For each item, complete the table of values and use the results to estimate the value of the limit.…

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Q: Use the Squeeze Theorem to calculate the limit. lim x sin

A: Given limit

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

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Q: Use the &-8 definition of e limit to prove lim+1 =2. x→5 5 nd the ɛ value when &=0.001.

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Q: Find the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R.

A: We find the pointwise limit  lim_(n→∞)(ex/n/n) for x ∈ R.

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

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Q: 4. Do you agree with the following statement? When a function f is continuous at a number a, then it…

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Q: Use the e – 8 definition of the limit to prove that lim x2 – 2 = 2. %3D - x→2

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Q: Find the limits in Exercise

A: Given: limθ→π4tanθ-1θ-π4

Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: Evaluate the limit: lim1-cos 3h h

A: Given

Q: Find a formula for a function f that satisfies the following conditions. lim fx) = 0, lim f(x) - -0,…

A: Function

Q: Calculate the limit and show proof. lim (1,1)(0,0) r2 + y?

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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: Use the graph to compute the quantities asked for. y lim, 3 f (x) does not exist -1

A: our objective is to find the limit

Q: Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths in…

A: We have to explain why fx,y must approach a unique L as x,y approachesa,b along all paths in the…

Q: Use L’Hospital’s Rule to find the limit.lim x → ∞  e^2x − e^−2x / ln(x + 1)

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Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim…

A: Here we have to evaluate the limit of given function

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

A:

Q: show that L’Hôpital’s Rule is applicable to the limit as x →±∞and evaluate

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Q: Use l’Hôpital’s rule to find the limits

A: Given: limx→0x2x2x-1 To determine: The value of the given limit. Concept used: L'hospital's rule…

Q: Does L'Hôpital's Rule apply to lim f(x)g(x) if f(x) and g(x) both approach oo as x → a?

A: L' Hopital's Rule is used in the following cases,

Q: T is discontinuous at -1 because lim f(x) as x--> -1 does not exist. * %23 .7. 5. %23

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Q: Use L’Hôpital’s Rule to evaluate the limit.

A: the given limit is: limx→∞xe-x2 we have to evaluate the given limit by using the L' Hospital's rule.…

Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

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Q: Use the formal definition of the limit to prove the statement rigorously.

A: We know               -1≤sin 1x≤1 ⇒-x≤x sin 1x≤x

Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

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Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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Q: Use l’Hôpital’s rule to find the limits

A: Given: limx→11x-1-1lnx

Q: X- 2 a lim " +x-6 T0 – x - 4 sin 2x b. lim c. lim x+ 6

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Q: Use l’Hôpital’s rule to find the limits

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Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

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Q: What is the the value of the limit lim,0 Vn (Vn+1- /n)? Show your work.

A: