Зx2+kx+k+3 lim X→-2 х2+x-2

Q: 65. Is there a number a such that 3x2 ax a + 3 lim +x-2 exists? If so, find the value of a and the…

A: Refer to the question, we have to find the number ‘a’ such that limit exists .

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: Evaluate the limit, if it exists.

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Q: The value of the limit 3 lim (1- z/2 is equal to O e-3/2 O e3/2 O e2/3 O 1 The limit does not exist

A: Given: The limit limz→∞1-3zz2.

Q: Prove, using the e-d definition of limit, that: (a) lim x² + 1 = 2 24-1

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Q2) Evaluate the limit at x = -2 for: x 1 2x2 4x - 8 S(x) x² - x- 6

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Q: Find the limit (if it exists) of A"x, as n approaches infinity, where and x, = a

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Q: Find the limit, if it exists. x2 - 36 lim X6 X-6 O12 ) 1 Does not exist 6. OOOO

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Q: (3x²+kx+k+3` lim x→-2 x2+x-2

A: Given

Q: For what value of the constant k such that the following limit exist: 2x+x lim |(x² – 2+k)

A: We have to find the limit of the function 2x+xxx2-2+k as x tends to 0, where |x| denotes the…

Q: Using the precise definition of a limit, à in terms of & for lim (2-3x) = -4 is E/-3 X-2 A) True B…

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Q: Find the limit.

A: The given limit is, L=limx→2+e32-x=limx→2+e-3x-2

Q: 7. Find the limit, if it exist x² +2 a. lim xV9 - x? C. im b. lim * x-1

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Q: Prove, using the e-8 definition of limit, that: (a) (b) lim ²+1=2 24-1

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Q: Find the limit L. Then use the e-8 definition to prove that the limit is L. lim (r + 4)

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Q: 1. Find the following limits mathematically. If the limit does not exist, state why. x* - 4x -12 a.…

A: When applying the limits to an expression and if we get a 00 form then use l'Hopitals rule to find…

Q: Use the e-N definition of limits to show that 2n -15 lim = 1. %3D n0o 2n - 13

A: The objective to show that limn→∞2n-152n-13=1.

Q: Find the limit , if it exist x-13 lim |x-13| a=13. X-a O a. D.N.E O b. 1 Oc. -1 O d. 0

A: Solve limit

Q: b) Use the concept of infinite limit to compute the following: (1 – i)z + i lim 2-i/2 2z +i

A: To compute the limit: limz→i21-iz+i2z+i Explanation: The concept of limit states that if the highest…

Q: d) Evaluate the limit lim msec(x). x5

A: In the given  question  msec denotes the slope of the secant line joining the points (5, f(5))…

Q: 3. Using the definition of the limit, and given that lim 2* x- 2 for any N > 0, there is a ð > 0 so…

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Q: Q/Calculate the limit statement lim l है 7) X → -

A: The objective is to evaluate the given limit. Lopitals rule states that limx→af(x)g(x)=LIf f(x)→0,…

Q: Determine the Infinite limit. 9- x lim X8 (x - 8)2 O 00

A: In this question we have to determine the infinite limit if it is positive or negative.

Q: Find a value of the constant k such that the indicated limit exists. 8 -5 lim x-0 ekx +5

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Q: li'n -3Carl) lim -3n-3 ヘ→ 0 ヘう o

A: Yes. It is -3. Just take n common from both numerator and denominator and then put n tends to…

Q: Evaluate the limit, if it exists. If not, enter "n" below. (4 + h)-1 – 4-1 lim h>0 h

A: Evaluate the limit  given that. Limh-0 (4+h)-1 - 4-1/h. In this we use L'hospital rule.( When become…

Q: A. Use the limit definition to find w = 3x²y - 5xyz + 10 yz? given a wl

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Q: Evaluate the limit, if it exists. If not, enter "n" below. (6+ h)-1 – 6-1 lim h→0 h

A: The solution of given problem is :

Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: Find the limit, if it exists.

A: Given: L=limx→-∞5x2x+3 For evaluating given limit, we simplify given expression and evaluate the…

Q: Using the e - N definition of a limit, prove that 8n lim n+00 4 = 2 4n – 1 -

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Q: Use the e - 8 definition of the limit to establish a ô that proves lim (x – 1) = 2 x-2 O A) 3 B) 2e…

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Q: Find the limit given by 1 + n + 2 1 lim n + 1 2n n→∞

A: The limit of the function at a point is equal to the value of the function when the value of the…

Q: (b) Deduce the limit of - II (--) k 1 + n2 Un k=1

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Q: Find the limit. lim e8/(5 - x)

A: Given,  limx→5+e85-x  We have to find the limit.

Q: 9. Find the limit if it exists, either as a number or an infinite limit. lim (Vx? + 3x +7 – x)

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Q: Evaluat the limit si a. lim (Itx)"-1-nx ー1-nx x2 メ

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Q: show that the limit of a^n/n! is 0 as n approaches infinity

A: Gien To find limn→∞ ann!

Q: 3 Evaluate the limit lim [(2-1)(3– 2i)+1–3i] and use the definition of the limit (e-6) z-2+i to…

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Q: 1. By referring to Figure 1; x = 1 x = 3 y = h(x) (2, 0) (0, –) - Figure 1 a. List the x values that…

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Q: 8. Find the limit, if it exists, or show that it does not exist: 2х-у a) lim (x,y)→(1,2) 4x²-y2…

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Q: Find the limit. -重班 4x + 4 x² + 2x lim x-2+ Does not exist 4 O- 1

A: Find the limit

Q: What result do you obtain when you evaluate the limit (RHL and LHL) of the limit of (x^2-16)/(x-4)…

A: Given f(x)=x2-16x-4 LHL=limx→4-f(x) and RHL=limx→4+f(x) Here if LHL = RHL, then limit exists.

Q: Find the limit. a(x + h)³ – ax³ lim h

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Q: Can anyone solve this question please ? Many Thanks

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Q: Find the limit. lim x5 In x x-0* O 1 O 5 O-1

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Q: # 11. The lim,→-4 x²+ cx+c+5 x² + 5x+4 exists. What is the value of “c“? What is the value of the…

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Q: Find a value of the constant k such that the indicated limit exists. 5* – 1 lim x→o eka + 8' k =

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Q: 12. Find the value of the limit: lim a. +00 b. -00 d. Indeterminate

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.