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

Q: (a) log,(5x – 1) + 6 = 9 (b) 163x+1 = (4)*-1 %3D (c) In(x + 6) = In(11) – In(x – 4)

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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: Find the integral: log7 X dx = %3D

A: Solve the following integral

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: 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&gt;0 To show  log1+x=x−x22+x331+θx3 for 0&lt;θ&lt;1 and log1+x&lt;x−x22+x33…

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: Whats the integral of (log_base8(8x))/x dx?

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

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

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

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Q: A. Differentiate and simplify the result. 1. y = V4x + 3 log2(x² + 2) 2. y = 3vx2-3x+1 3. y =…

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Q: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

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Q: Evaluate the integral. 8 r log 4(x + 8) x +8 xp-

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Q: Differentiate  f(x)  = log 10  ( 2+ sinx )

A: Rewrite the given function as shown below: fx=log102+sinxfx=ln2+sinxln10        since logab=lnblna

Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: f(x) = (a

A: Here, let y=f(x)=x3x3ex3 Taking natural log (ln) on both sides: ln y=lnx3x3ex3⇒ln y=lnx3x3+ln ex3⇒ln…

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

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

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

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Q: Evaluate : |(log x)sin' x dx

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Q: Differentiate log sin x by first principles.

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

A: Answer : False

Q: Express th equation in exponential form.

A: Logarithm equation can be converted to exponential using the following properties of a logarithm.…

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: dx Evaluate log - 1+ax 1-ах

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

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Q: Find all vawes of k don uhich log kx 112 log (x+) has one soluhion

A: Just use basics of logarithm.

Q: calculate the integral.

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Q: Hw) Prove That:- 0 sinhz = log (z+lz*+) e coshz= Loy (2/23) ® Tanh'z = +2 1-2 Examml

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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

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Q: Prove 42 tan xdx =1-log 2

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Q: 2 log(x+y) = 3log3 +logx + logy

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

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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: Vx²-1•sin x y%3= %3D (2x+3)4

A: To find: The derivative of y=x2-1·sinx2x+34 using logarithmic function. Formula used: The derivative…

Q: ` log x dx

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Q: Find the derivative of Log(22³). 1/22 3/z 2/z

A: Given problem is  : ddzln2z3

Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

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: 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: 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…