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

Q: If w=log(ysinx+xsiny) then prove that wxy=wyx

A: If w=log(ysinx+xsiny) then prove that wxy=wyx

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

A: It is logarithms problem.

Q: Use the trapezoidal rule with five function values, together with appropriate log laws, to show that…

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Q: Prove that all exponential functions are not of the same growth order up to big theta (when a and b…

A: Plot the two exponential functions f(x) and g(x) for a > b.

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: 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: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: Note that lim (1 - 7x)1/x is indeterminate of type 1°. Using logarithms, we have In(1 – 7x). As x-…

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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: Use mathematical induction to prove that the derivative of f (x) = x^n equals nx^(n-1) whenever n is…

A: Given: P(n) be the statement derivative of f(x)=xn is equal to nxn-1, where n is a positive integer.

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: e3+j4(3+ j4)5 log ji' sin(3 + j4) j2022

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Q: Use logarithmic differentiation to find dr y = (x'+x}/x³ +6 Oa. ( 3x²+1 3x² 2x³ + 12 ´ 3x² + 1…

A: first use logarithmic property and then differentiate it.

Q: () N f(x) = , show that f(0) and its leading differences form a geometr 5. (i) Prove that A log x…

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Q: PROVE that log5 100 = 2(1 + log5 2)

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Q: If H(x) = logb 1/x, show that H(b-1/z)= 1/z

A: H(x)=logb1x, we have to show that Hb-1z=1z

Q: f (x) = In(x + 4) + 3 %3D f(2) 3 e2-6- 4 %3D f (x) = log(a- 2) - 8 %3D f (x) = 108+2 ----- f (x) =…

A: Some functions are given and the inverse of the functions are also given. We have to check that…

Q: 1+ax dx Evaluate log 1-ax x 1-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: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

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Q: In LRT reject H, when Ais small, so we reject H, when the value -2 log A is small Select one: True…

A: Answer : False

Q: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: Prove that : log 2 xp

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Q: [E] Prove with usual notations that (i) hD = log(1 +A) = – log(1 – V) = sinh '(u8)

A: We will prove the following result.

Q: Show that f(x) =12(logx+1)+x² -10x+3 is a maximum when x=2, a minimum when x=3;

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Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

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Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

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Q: Show that || (A(st) + A(s)A(t)) dsdt = 2.x log x + 0(x) as x → 0o. JU(4)| log°x s 2 // |u() dsdı +…

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Q: Solve the problem in a paper and upload as pdf document If f(x,v) = log,(3x), Verify fxy=fyx ху

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Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

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Q: Evaluate sec(log x) -dx x In | sec(log x) + tan(log x) | +C 1 log e In | sec(log x) + tan(log x) |…

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Q: Prove the third law of logarithms. [Hint: Start by showingthat both sides of the equation have the…

A: To prove this, we show that the derivative of both sides of the equation is same.

Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

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Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

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

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Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Verify Lagrange's mean value theorem in f(x) = x²+2x-1 in (0,1)

A: We have ,  f(x) = x2 + 2x - 1    We know the , Lagrange's mean value theorem, If a function f is…

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: Prove 42 tan xdx =1-log 2 3

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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: d log, x = 1 dx [(In a)(x)]

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Q: Prove log (AB) = B log(A)

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Q: Use mathematical induction to prove that the derivative of f (x) = x^nequalsnx^(n-1)whenever n is a…

A: The principle of mathematical induction is used for proving any mathematical statement. First, an…

Q: Show beta (a,b) belongs to the z- parameter exponential family.

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

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