SK YOUR TEACHER PRACTICE ANOTHER Prove the statement using the , definiton of a lmt. lim -2x - 8 X-4 Given e> 0, we need &0 2- 2x -8 v Such that O 4 then -6 We have *-4 x2- 2x -8 -4 21 - e 2-6e - O *-4 x-4 8- Selectv Then 0 -4<6- I-4«dete - t definition of a limit, im 2-86. Reed Need Help? Vieing Saved Work evetoLast esona Submit Answer

Q: نقطتان )2( * .Find the limit Given lim, 0- f(x) = L1, lim,-0* f(x) = Lr, and L1 # Lr, which of the…

A: Here, the left hand and right hand limits exists but not the same.

Q: Is there a number a such that Зx? + ах + а + 3 lim x? +x – 2 1--2 exists? If so, find the value of a…

A: We have given;

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: 32 Evaluate the limit, if it exists. (x + h)³ – x lim 3 h

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Q: tan x lim 4-V lim x-16 16x-x² x² -9 lim x-3 x²+2x-3

A: Find the value of limit limx→πtanxx. limx→πtanxx=tanππ             =0π            =0 Thus, the value…

Q: 5. Evaluate the following limits 3x2(x – 1) 400 5x(2x2 + 1) 2 – x3 (a) lim (b) lim - 2x + 5 x – 2…

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

Q: 5. Evaluate the following finite or infinite limits. 5x²+3x+2 a) lim x- o 2x2-x b) -5x3+3x+2 lim x→-…

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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: Evaluate the limit. N 13i lim N-00 N2 i=1

A: First get the value of summation and use sum of first N numbers = N(N-1)/2

Q: ind the indicated limit, if it exists. (If an answer does not exist, enter DNE.) lim x→∞  x2 x2 − 3

A:

Q: Evaluate the following limit:  the limit of 3x(e^(1/x))-3x as x approaches infinity

A: Given information:The given limit function is .

Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: Exercises find the Limit using o Lim 2_4 メ→2 x*+2ズ-8

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Q: e) Evaluate the following limit at infinity and show your work. 3x3-4x a) lim x→∞ x²-2x³

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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: x+2 6. lim x-→2 x? - 4 3+x- 7. lim Jx? -9 8. lim x-3* x - 3

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Q: Using the ε − N definition of a limit, prove that lim(n→∞)=(6n^3 −2n+1)/(2n^3+1)=3.

A: In the given question we have to prove the following limit by using ε-N definition…

Q: 5. Is there a number a such that Зx? + ах + а + 3 lim x→-2 x? + x – 2 | exists? If so, find the…

A: Topic:- calculus

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…

A:

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

A: Given that       limx-&gt;2+ (-7)/(x-2) = -∞ .

Q: Find the following limit: lim f(x) X-2 ОА. 2 О В. -2 OC. 0 O D. The limit does not exist

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Q: Evaluate the limit In(x) lim x+1 x2 - 19x+ 18 a. 1 19 O b. 19 C. 1 17 O d. None of these. е. —17

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Q: Use the definition of limits (ε-N) to show limn→∞ ((n/(2n−1)) = (1/2).

A: Find the subtraction value of sequence and limit

Q: 3. Using the definition of the limit, and given that -7 lim x-2+ x – 2 - 0o, for any N > 0, there is…

A: Given that         limx--&gt;2+{-7/(x-2)} = -∞

Q: What value(s) of o are an appropriate choice when proving the following limit? lim (2 + 9x + 25) = 5…

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Q: Complete the table and use the results to find the indicated limit. x3 If k(x) = 46x - 144 find lim…

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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 In(x) lim x²-21x+20 X-1 X O a. 21 1 O b. -19 Ос. 21 O d. None of these. е. 1 19

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Q: Calculate the following limits, or explain why they diverge. Зn? + п — 1 lim n0 -2n2 +n – 4 x² – 9…

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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: Calculate the following limits, or explain why they diverge. 3n + 6ni lim n0 12+ 3i|n 2n² – 2 lim…

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Q: lim x2 - 6х +9 2x -x-21 lim x-3 9-х2 1-sin x lim x- cosx

A: Given: The given expressions are, limx→5x2-6x+9 limx→-32x2-x-219-x2 limx→π21-sinxcosx The…

Q: 1) Find the limit as x approaches 2 from the left and from the right (if they exist). Does the limit…

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Q: 1. Evaluate the following limits or show why they do not exist (a) 3r +1-1 lim 2r -4

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Q: Find all values of c such that the limit exists.

A: To find values of c such that the limit exist limx→1x2+3x+cx-1

Q: Prove the following using the definition of a limit. n - 1 (a) lim 1 n+on+ 1 (b) lim (2x² − 3) = −3…

A: Given a) limn→∞n-1n+1=1b)limx→0(2x2-3)=-3c) limx→2-1x2-4=+∞

Q: Using the definition of the limit, and given that lim 00, r any N >0, there is a ô > 0 so that the…

A: Given limit is limx→2+-7x-2=-∞. We know that for a function fx, we have limx→a+fx=-∞ if for any…

Q: 3. Evaluate the following limits, if they exist: 1 (a) lim 1 +3 2x x→-0

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Q: If n is any positive integer, then the limit lim x→0+ xn ,what is the limit? O +00 Indeterminate

A: Given: Let y=limx→0+1xn, Where n is any positive integer. To Find: To evaluate the given limit.

Q: Use the properties of limits (p. 100) to evaluate and completely simpl (e2x lim 4x In e 3x ive an…

A: To find:limx→12e2xx2+4xlne3x

Q: a) What is the definition of limit? b) Evaluate the following: 6+ 4t lim t--3 t2 + 1

A: Given: limt→-36+4tt2+1

Q: With regard to the limit lim x² = 25, Find a 8 such that |x² – 25| < 10¬3 if 0 < |x – 5| < 8.

A: We are given limx--&gt;5  X^2 = 25 We have to find delta , and we can find it by applying definition…

Q: 8. Employ the dividing out technique to evaluate the following limit: 2x? +x- 6 lim - x+ 2

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

Q: (- 2+ h)? – 4 Evaluate the limit: lim h→0 h

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Q: 4. Use the definition of limit to prove each of the following. a) lim (5x- 11) = -1 d) lim x = 2 b)…

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Q: 5) Evaluate the following limits x2 lim x→-0 e

A: We have to find the limit: limx→-∞x2e-x This is ∞∞ indeterminate form so we can apply L' Hospital's…

Q: 1. Evaluate the following limits by applying the limit theorems (show solutions): 2. 7. x→4 V4x 1 1…

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

A:

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.