az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

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: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: If X~U(0,1) then Y=-In{1-X)~ Exponential (^) Pleose Show

A: When two random variables are connected by a bijective mapping and the probability density function…

Q: H.w find the root fcx)= X log x-loo when [ !,3} by Bisaction ?

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Apply the formula deduce that (x) log x + [A(n) () = 2x log x + 0(x) n n≤x as x→∞o, where y is…

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Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

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: Express th equation in exponential form.

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Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

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Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

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Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

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Q: Compute the deriv: (c) y= log2 |¤|

A: Here we have to compute the derivative  c) y=log2x d) y=x3-1x4+1

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

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Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

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Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

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Q: If y = log, x then x = y* %3D %3D Select one: O True False

A: Given that ,                 Now, by the definition of logarithm, if and only if       Here,  and…

Q: If Y = Ab" , then log Y = n log(Ab). %3D

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Q: Show that log, (x + Vx² – 1) + log,(x – Vx – 1) = 0.

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

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

A: We will prove the following result.

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f(x)=log(x²+1)-log(2) on [-1,1]…

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Q: dy Solve the initial-value problem for y as a function of r. (4 x) = 1, y(0) = 4 de…

A: Given initial value problem is,

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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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: . if võ =o, i =1 and Ju = 2 estimate 13 %3D by constructing Logrange polynamial, Itn with the exact…

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Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

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

A: Solution Answer. True Because LRT is the likelihood ratio test and given statement says that the…

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: 8. Let b be a positive real number not equal to 1. Determine the solution of the equation log, (2z –…

A: See the solution step by step.

Q: Solution to the equation Log(2iz + 1) = in is None of them z = ni z = i

A: Usually, log x is represented as log10x . If log x=y , then x=10y .  The natural logarithm, ln x is…

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: Finds 군x, 군y, Zxx, 군yy, 근xy, 2sx Z = LogX

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Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: Consider the function g defined by 1 g(x, y) = cos (Tx VT) + log3 (x – y)" Determine

A: We can solve this as follows:

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

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Q: If y = log x + ex then dy/dx = log x + ex a. True b. False

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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: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

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

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Q: Given that log, x + 2 log4 y = 4, show that xy = 16. Hence solve for x and y in the simultaneous…

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Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

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Q: t(z)= 2z log2z  , t '(z)?

A: