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

Q: ,2,3 Expand into several logarithms: x'y In 25

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: 4 If log,(x + 1) – log,x = 2, then x equals: F H

A: It is logarithms problem.

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

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

A:

Q: The logarithmic expressi on In can be rewritten as (1) 3ln y- 2 In y- 6 (3) 2 1-6 In y (2) 2 (4) Vin…

A:

Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: Determine the maximum and minimum values of the function f(x)= -4 x log2x on the interval [1,4]

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Q: The union of left ray topo log y and right ray top log y on real numbers is usual topo log y True…

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Q: Assume that your utility has a natural log function U(W)=ln(W), which is a concave function. Your…

A: Answer:----.               Date:----11/10/2021

Q: 4. Differentiate the function. f(x) = log3 (x In x)

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

A:

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: Disprove the statement log(x + y) = log x + log y by, a) Letting y equal a positive constant of your…

A: Given  The statement log(x + y) = log x + log y

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: y = log (4x°)

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

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

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

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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: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

Q: Graph the function, not by ploting points, but by starting from the graphs in the figures below. gx)…

A: Given function is gx=log2−x. We have to draw the graph of the function gx=log2−x. The graph of the…

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: 22. Suppose f(x) = log x + log(x – 3). Find the x-value for which f(x) = 1.

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Q: 4. Show that id 5D accuracy is required to calculate the value of log(1+x) at x=0.1,0.5 by using the…

A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

Q: (b) 2log(x – 3) – log(x – 1) = 0

A:

Q: 4. What is b if (log, x)' :? Зх

A:

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

A:

Q: Differentiate the following and simplify: y= log, (sinhe") h(x)=3sinh(1–3x² )cosh(1– 3x² ) 1. 2.…

A: As per bartleby guidelines we only give first question answers.

Q: Show that (1+:)'→e. as x → o, → e. HINT: Since the logarithm function has derivative 1 at x = 1, %3D…

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Q: Given the functions f(x) = log₂ (2x) and g(x) = 2x - 3, which of the following statements is true?…

A: Here, the given functions are f(x)=log2(2x) =ln (2x)ln 2(used change of base)& g(x)=2x-3 Here,…

Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у…

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Q: 17. The product rule does apply when multiplying exponential functions with sinusoidal functions.

A: Yes the product rule applies when multiplying exponential functions with sinusoidal functions

Q: 6. Which of the following functions grow faster than In x as x→∞? Which grow at the same rate as In…

A:

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

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Q: Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3)…

A:

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: п/4 Show that log(1+ tan8)d = log2. 8

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Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

A:

Q: y = Arccos (logx); y' = * %3D

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

A:

Q: 7. Find y'. y = log, (9– x-x)

A:

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

A:

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

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

A:

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

A:

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: Let X1 be exponential with mean 4 and X2 be exponential with mean 6. Assume X1 and X2 are…

A:

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 .