Calculate the limit of log3 x as n – ∞ O 3 8

Q: Ex 11.1.3 Determine whether {Vn 47 n converges or diverges. If it converges compute the limit.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (h) lim - 7 log: (z) -0- ||

A: Given query is to find the value of indicated limit.

Q: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: dæ x-1 1

A: Solution: The objective is to find whether the given integral converges or not

Q: Let x1 = 1 and xn+1 1 for n e N. Show that this sequence is convergent and find its In + 2 limit.

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Q: Find the radius of convergence as n goes to infinity of (log n)2 xn.

A: The given series is                                     ∑n=0∞log n2xn

Q: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

Q: xp Vx(x + 5) converges O diverges

A: CONVERGES

Q: 1 -dx xln*x 1.

A: To determine if the following is a convergent or divergent. ∫e∞1xln4xdx Solution: A indefinite…

Q: Graph the function. Label the asymptote(s). 11) f(x) = log4 (x - 2)

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Q: Employ the concept of growth of functions to compute the smallest intege for which the function f(x)…

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Q: Find the value of a so that Screen Shot 2021-10-06 at 8.48.07 AM.png ... зах2 —4х + 7 4 Зx2 — 5х —1…

A: We have to find

Q: What is the time complexity of the following function: f(n) = 100 - n O o(n?) O O(nlogn) O O(n) O…

A: Here it's given f(n)=100-n which is a linear function.

Q: Use limits to prove the following asymptotic statements. 1. V4n2 + 1 = ©(n). 2. n" = Q(n!). 3. Vn +…

A: To determine, if two functions f(n) and g(n) are Big -O and Big-Θ follow the rules as stated:  1.…

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: Select the following asymptotic estimates that are valid. log(n") n² = O(log(n!)) √n³ + 2n³ + 1 =…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: 1. Let f(x) = log2(x). II

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Q: Which of the following statements is TRUE regarding the function f(x) = log2 (x + 4) + 3? There is a…

A: Horizontal asymptote  of a function is a line y=k that tells the behavior of the function at the…

Q: find the formula for an exponential funtion that passes through the two points given  (x,y)=…

A: Given  (x,y)= (0,6600) and (x,y)= (2,66)

Q: Find the value of a so that Screen Shot 2021-10-06 at 8.48.07 AM.png ... 3ах2 — 4х + 7 lim log3 = 4…

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Q: Evaluate the limit as x approaches infinity of log7x/log8x

A: We need to evaluate the given limit

Q: Q 3/ A- Find lim,3 B- log10 (3x – 7) + log10(3x + 1) = 1+ log10 2

A:

Q: Which of the following graphs has a vertical asymptote at a = 4? O y = log(x) + 4 O y = e-4 O y = 4"…

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Q: (i) Find the constant term in the expansion of x+-

A: You have given 3 different questions in picture, without mentioning any particular questions. We can…

Q: O Give a big-O estimate for f(n) = 3n log(n!) + (n²+ 3) logn.

A: Big O notation is a mathematical notation that describes the limiting behavior of a function when…

Q: Graph the function f (x) = 2 log5 (-x - 1) - 8 on the axes below. You must plot the asymptote and…

A:

Q: Let x1 O and xn+1 x+1 2 Show that (x,n) converges and find its limit.

A: It is given that  x1=0 and xn+1=xn2+12. Let xn+1=ϕ(xn)=xn2+12 By fixed point iteration method…

Q: For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on…

A: Use continuity definition of function

Q: How large does x have to be, so that e^(-x/10)<0.1?

A: We need to find the values of x for which the following inequality holds good.

Q: Find the smallest positive integer n so that f(x) = x8-log(x³ ) + x6-log(x5) is big-O of xr.

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Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

A:

Q: 4. Show that the function log(1+ x) lies between functions x - and x for all x > 0. (Hint 2(1+ x)…

A: We will expand log(1+x) by Maclaurin's series. Let f(x) = log(1+x)

Q: Determine the O-class of the function h(n) defined by if n = 1 h(n) |h(L)+h([1) + log n if n > 1

A: We will first do a clever substitution to convert the given piece-wise function into a recurrence…

Q: If n is a power of 2, prove that M(n) = (n log n) / 2 , using Master of Theorem method. Show all…

A: Given:n is a power of 2To prove:M(n)=(nlogn)2using Master of Theorem method.Proof:Inorder to prove…

Q: 5x + 2 lim log + 6 10x + 12 ° X-

A:

Q: What transformations would map the graph of f (x) = log3 (a) onto the graph of g(x) = log3 (81z³)?

A: Given data fx=log3x gx=log381x3

Q: Find lower bound for f(n) = 5n².

A: To find the lower bound for f(n) = 5n2

Q: 5. Prove that if {a,}f° converges to 1, then {an}° converges to 1. Hint: You may use a logarithm…

A: If an1∞ converges to 1, then an1/21∞ converges to 1.

Q: Show that g(n) = 3" + 1010" is asymptotically bounded above by f (n) = 4".

A: Given, gn=3n+101010fn=4n Now, divide gn by fn we get,…

Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

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Q: Find the domain of each fucntion: a.) f(x) = ln(2-x) b.) f(x) = log2(2x-3))

A: Calculation:Note that the argument of the logarithm function always positivea.) The domain of the…

Q: Show that (- 2-1)* log k converges. k2 k=1

A:

Q: 11 dx Determine whether is convergent or not. (3 – x)2/3

A: As the value of Integral is finite, it converges.

Q: Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80…

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

A: Given: The limit expression as limx→∞log2xlog3x+3, To find: The value of limit using L'Hopital's…

Q: Find the value of a so that Screen Shot 2021-10-06 at 8.48.07 AM.png 3ªx2 – 4x + 7 lim log3 = 4 3x2…

A: NOTE: As per our guidelines, I have solved first problem. If you want the answer of other, kindly…

Q: Find the least integer n such that f(x) is O(x") for the function 3x +x log ax

A: This is a problem of finite math, and complexity.

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x>0 The function f(x)=x is defined for x≥0 Note: If logba=c…