Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o more slowly than any power of x.

Q: Use the one-parameter regular exponential family definition to find the functions, h(x), c(0), w(0)…

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Q: 9. What is the maximum value of |Log z| |2| 1? on

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Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: a- Simply the following 1 1. Inx – In(x2 – 1) + 2ln(x + 3) - 2. 5log2 + log3 – log8 b- find x for…

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Q: 5. Suppose that A = Use the definition of the exponential to calculate exp(At) in terms of familiar…

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Q: Find a number E such that log (5z + 1) = 2

A: The solution is given below.

Q: The Gutenberg–Richter Law states that the number N of earthquakes per year worldwide of Richter…

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Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

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

A: There should be correction in the question that x tending infinity.    As there is nowhere 'n'…

Q: log(1+e¯*) is The indeterminate form of lim,→∞

A: The form is:-

Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: Given that a and b are real and unequal and that logab + logba2 = 3, find a relation between a and b…

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Q: b) Expand log(a+h) by Taylor's Theorem.

A: Consider the expression: loga+h ……1

Q: Prove that Log(2) is discontinuous on R, the nonpositive real axis.

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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: Prove that | log,x| E O(log2 x )

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: To Discuss: a. Does fx=logarithm x, with base 12 approaches a certain real as xincrease positively?…

Q: The natural logarithmic function f(x) = In x has the asymptote x =

A: Given: f(x)=lnx To Find: Asymptote of f(x). Concept: Vertical Asymptote: x=c is called vertical…

Q: Prove: logaxr = r loga x.

A: Given equation: loga xr=r loga x

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: Prove that : log 2 xp

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Q: Prove that In x lim xP for any number p > 0. This shows that the logarithmic function approaches…

A: Prove that limn→∞ ln xxP=0for any numbers P>0

Q: (b) Use L'Hospital's rule to determine the following limits: log2 x (ii) limx° log3 x

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Q: The logarithmic function f(x) = In(x – 1) has the asymptote x =

A: Given: fx=lnx-1 we know that lnx has the vertical asymptote x=0 similarly, given function has the…

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: - If y=a² 1-log.x and z=a* 1-log, y , then x is equal to

A: Introduction :

Q: Suppose that f (x) is O(g(x)), where f and g are increasing and unbounded functions. Show that log…

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Q: 5. Find the domain of f(x) = log(x-4)

A: The given function,   f(x)=logx-4

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

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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: Determine the maximum and minimum values of the function f(x)=-4 •log 2x on the interval [1,4]

A: Given function is  on interval [1, 4].

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

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

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Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

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Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

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Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

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: Prove that A log ƒ (x).= log|1+A7®) f(x)

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Q: B. Evaluate the following limits of Logarithmic functions 1. lim(log2 2x) 4

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Q: 12) eiven AMUEÍVRTAMA, S C«) X22x<0 2x+1, 0<xL2 a) Evaluate f at x = -1,0, and 5. If not defined,…

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Q: What is the linear approximation of log base 5 x at x=5

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Q: Use values of f(x) = In(x) %3D to estimate log ( 6.67 ) using 4th order

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Find for the following function: 3- y = log,(x - x) 4- y = In2

A: It is an important part of statistics . It is widely used .

Q: (a) Prove that log₁ x= -log₁ x where a > 1. a

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