verify whether the limit to infinity of n(n + 1)(n + 2)−¹(n + 3)–¹ is equal to one.

Q: Find the limit  x appraoaches infinity (e 3x  - e -3x ) / (e 3x  + e -3x )

A: limit  x approaches infinity (e 3x  - e -3x ) / (e 3x  + e -3x ) To find the limit => Take the…

Q: Find the limit algebraically. 2x lim 16 -x - 4 O - 16 O 16 O -8

A:

Q: Solve the following limits by algebraic method and by the corresponding theorems √9x +4-2 a) lim…

A:

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: Evaluate the limit A. ƒ(x) = 5x + 2 at x = 3 x²-9 B. f(x) at x = 3 x-3

A: A. f(x)=5x+2B. f(x)=x2-9x-3

Q: Find the limit. /h² + 10h + 11 - /11 lim h→0* h² + 10h + 11 - /11 lim h h→0*

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

A:

Q: Find the limit. 시h2 + 10h+ 19-119 lim h vh? + 10h + 19 - /19 lim h h→0* II

A: Given: Limit equation is given.

Q: Evaluate the limit of 6/x^2 as x approaches 0

A:

Q: Find the limit of (2n!/n!n!)^1/n as n approaches infinity

A: Here we find the limit of (2n!/n!n!)^1/n as n approaches infinity

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

A:

Q: Determine the infinite limit. 2+ 4x lim x-2 x - 4x + 4 00 8 O O

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Q: Q4\ find limit of the following x² - 2 1- lim Vx-2 X2

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Q: Compute the limit as xà0 of f(x)=[(9+x)^(1/2)-3]/x, if possible.

A:

Q: 2. Evaluate the following limits. 4x2+x-7 f. lim 2x2+3x+10 X→-00

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Q: Find the limit. 2 lim (2x - V4x - 3x + 2) O A. - 0 В. -2 С. О 3

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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: What are the limits of both parts of this question?

A: In part a, there is no bound, so the answer of the limit is infinity.

Q: Find the limit of 1/n(n!)^1/n as n approaches infinity

A: We find the limit of 1/n(n!)^1/n as n approaches infinity

Q: (iv). limit x-0 ²-1 - x - x ²³/₂2 - x² - x ²%/ e 6 x4

A:

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

A: Given: limx→cx2-5x-6x-c for finding value of c for given limit to exists, we factorize numerator of…

Q: 7. Find the limit. (Let c and d represent arbitrary real numbers. If an answer does not exist, enter…

A:

Q: 8. Evaluate the limit of (4x^2-x)/ (2x^2+4) as x approaches a. a. 2 b. 4 с. а

A: We have to find limit.

Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 2--2- r2 – 4x + 4

A:

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: The value of k such that x2 lim kx + 7 x→1 x – 1 exists is

A: Given: The limit expression limx→1x2-kx+7x-1, To determine: The value of k such that the given limit…

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

A:

Q: If the limit of f(x) as x approaches cis 0, then there must exist a number k such that f(k) < 0.001.…

A: Explanation: If limx→cf(x)=0, the for any positive ∈, (Like 0.001) there is a positive δ such that…

Q: Find the limit.

A: To evaluate the limit:limx→2xx2+1 Evaluating the limit. limx→2xx2+1=222+1=24+1=25

Q: 2. Evaluate the limits, if it exists. x²-6x+5 a) lim X-5 X-5

A: Given,  a lim x→5 x2-6x+5x-5  b limt→01+t-1-tt    We have to evaluate the limits

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

A: Gien To find limn→∞ ann!

Q: Find the limit, if it exists. Ilm x² 3x - 4

A:

Q: Compute the limit as x approaches zero of f(x)=(x^2+3x)/(x^2-x-12)

A: Given : Function f(x)=(x2+3x)(x2-x-12)   To find : Limit of given function when x approaches to…

Q: Find the limit. Iim (e 4/x x-0 9x) x/2

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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: Find the limit of f(x) = 9x+9/8x+8     as x approaches infinity and as x approaches negative…

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Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: 3x-2x+1 5. lim x-1 x+1

A: The objective of the question is determine the limits of the given functions.

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

A: Find the limit

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

A:

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: Evaluate the limit. x3 + x² + 9x + 5 lim 4 - 7x? 2 -00 Enter INF for o, -INF for -oo, or DNE if the…

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Q: Compute the limit as xà1 of f(x)=(x^2-5x+4)/(x-1), if possible

A: Topic - limits

Q: Can anyone solve this question please ? Many Thanks

A:

Q: a) Show that for any & > 0 and S₂ = ₁X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n n→∞

A: We will use Chebychev's inequality to find the limit of the given probability.

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

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Q: What is the limit of f(x) = 7 as x approaches ? (If an answer

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Q: - Evaluate the limit at x = -2 for: 31 2x2 - 4x 8 [(x) x² – x – 6

A:

Q: Find the limit as k approaches infinity for k ^(1/k)

A: Topic:- calculus

Q: f(x)=X÷2x if x 23 3x ifx<3

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.