9x e n.n (- 1)" g"x" O A. 2 n! n= 0 О в. 9"x" Σ OB. nl n=0 (- 1)^ g"x" O C. 2 nl n= 1 9x O D. E

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: Integrate 01-In x + C о √(5-2) x – 10 ln |x| X - - - 1 10 In |x| 2 25 Olnx-25x + C ▬▬▬▬▬▬▬▬ X dx. +C…

A: Topic = Integration

Q: a- Simply the following 1 1. Inx – In(x2 – 1) + 2ln(x + 3) - 2. 5log2 + log3 – log8 b- find x for…

A:

Q: The simplified form of In(÷-) using logarithmic rule is yz 4ln x+ In y- In z 4 In x- In y-In z 4ln…

A: The objective is to simplify the given expression using logarithmic rule. The given expression is

Q: Show that for 2 degrees of freedom, the probability P of a value 1 of greater than yo is ex and…

A:

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: A 200 g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138…

A:

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: Σ 3 to within 0.043 of its exact value. 3 Estimate the value of n =1 n

A: Solution::  Series Estimation:

Q: 2) A body temperature of 50 °F is placed in an oven whose temperature is kept at 150 °F. If after…

A: time required for the body to reach 100°F=?

Q: Express th equation in exponential form.

A:

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

A:

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: Express as a single logarithm. 5logbt-logb S + logb V - 4 logbu 1) logb 1/2 215 15 v1/2 ) 2) logb…

A:

Q: Express th equation in exponential form.

A: a). Given, lnx+1=2 The exponential form is, x+1=e2         ∵lnx=y⇒x=ey⇒x=e2-1

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

A:

Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: A 200 g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138…

A:

Q: Suppose that the number of bacteria in a culture at time r is given by N 3000(31 + te). %3D (a) Find…

A:

Q: 1. The solution to the cquation 53x = correct order on the right of the question. 4x+1 is given…

A: Re arranging steps in correct order,..

Q: 2 -3 r- 3 x = %3D (z + 4)- 1 = 24 --- log, 15625 6 X = !!

A:

Q: A sample of 600g of radioactive lead-210 decays to polonium-210 according to the function AcT) =…

A:

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: 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: 5) When a cake is removed from an oven, its temperature is measured at 300°F. Three minutes later…

A: Q5) how long will it take for the cake to cool off to 80F

Q: D.  Express as a single log and natural log :                ( log3 3 +   log3 6 +  log 3 2 ) – (…

A: Consider the given expression: log33+log36+log32-log318 Here, the objective is to express as a…

Q: -, State the transformations that are needed to turn y 4 log10(x – 4) into y = – 2 log10(x + 1).

A: Compare the both equation and take transformation and varify

Q: A sample of 600g of radioactive lead-210 decays to polonium-210 according to the function AT) =…

A: Topic:- exponential decaying function

Q: To ensure that the balls bounce consistently, tennis balls in Wimbledon are stored at exactly 68°F.…

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

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: Solve for x:   logx=0.328 logex= 1.627  log2 x=6 In x= 0.444 x=antilog 3 -antilog 2  if base…

A: We will do algebraic manipulations along with applying the properties of log & antilog And in…

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

A:

Q: Find the greatest integer less than or equal to log29 S² log2 (x³ + 1) dx + (2x - 1)³ dx.

A: At first, we have to evaluate: I=∫12log2x3+1dx + ∫1log29(2x-1)13dx

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

A:

Q: A positive integer is written on a blackboard. At each step, we are replacing the number on the…

A:

Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: Estimate (8.06)-/³ using differentials. (8.06)2/3

A: The given expression is

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

A:

Q: Show that 2 + 11n² log,(n³) – 7 = 0(n³)

A:

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

A: We have to prove the result.

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

A: