log; e(ln 5)(arccos(x)) simplifies to O a) 5 cos(x) O b) cos(x) c) arccos(x) d) None of these O e) 5 arccos(x) CoOS

Q: sun(log(1+z)) 230Log(1+ Suin2) um 2-)0 log(i+sinx)

A: We will use the result  If limx→af(x)g(x) = 00 , then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

Q: Express In(1+r²) +In r- In sin r as a singel logarithm.

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

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

A:

Q: Without using technology, please solve for the following equations for z exactly. (a) sin 2z = cosz…

A: (a) Given trigonometry equation is: sin2x=cosx To find the value of x in 0≤x≤π

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: 2 Solve log, (2 sinx) + log,(cosx) =-1, for 2n<x<-

A: According to Bartleby's guidelines. We are allowed to solve only 1 question ata time. Apologies for…

Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

A:

Q: 1. Show that (a) Log(-ei) = 1 - ži;

A:

Q: y = (cos(x²))* -2 Co:

A:

Q: log of the nth root of x equals log of x to the 1/n power and also equals to

A: The expression ax is the product of a with itself,  repeatedly x times. The function in the form…

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

A:

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: Solve for z.  Log(z)=1-i   (Also, is there a case where there are four distinct solutions?  Or…

A: Given logz=1−i We have to solve the equation logz=1−i for z Use logarithm property  logm=n⇒m=en

Q: dr 3. Verify that = ln(2). x(x+1) 1

A: Given: ∫1∞dxxx+1=ln2

Q: tan x dx = In|sec x|+ C

A:

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

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

Q: 2. Evaluate [log(-1-1)(-2-j2)] tan(4 + 3i) cosh-

A:

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: dx Evaluate log - 1+ax 1-ах

A:

Q: Use definition of hyperbolic function to show that 5e2z 1 2 cosh a + 3 sinhr Hence, solve the…

A: We need to prove: 2 cosh x + 3 sinh x =125e2x-1ex and then solve: 4 cosh x + 6 sinh x =ex This can…

Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

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

Q: The table shows corresponding values of x and y obtained experimentally. By drawing a suitable graph…

A: Estimate the logarithmic values of x and y. Tabulate the values of x, y, log10x and log10y.  x y…

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

A:

Q: Step 2 Solve the new integral using the General Log Rule. Then, back-substitute x into the equation.…

A:

Q: Solve for A: AR+AT=E

A:

Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: According to the properties of logarithms In sec x= - In cos x O True O False

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

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) |…

A:

Q: y = log sin x (csc 4x)

A:

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…

A:

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

A:

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

A:

Q: tan (log x) 2 dx 2 x(1+log*x)

A:

Q: 3 y = log ( cos DIFFERENTIATE THE GIVEN:

A: The detailed solution is given below Thank you

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

A:

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

A:

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

A:

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

A: We have to prove the result.

Q: The integral of the square root of the difference when the square of t is subtracted from 2, with…

A:

Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: log,(x – 5) + log,(x + 3) = 1 In(5x) + In x = In(100) In x + In(x – 1) = 10 In(x + 25) – In(x – 1) =…

A:

Q: The principal value of tan- (2i) is :Select one 1 +i-log, 3 .a 1 log, 3+ i- .b 2 2 c. None of these…

A:

Q: Determine the equivalent of log4i sin(3 – 4i). Express your answer in rectangular form.

A: The given problem is to evaluate and simplify the given complex expression and express in the form…