dx Q3/ find for the following functions ( choose 2 only ) dy A ) log5 (x + 1)² e) y=[in(x² + 2)*J* (1 + 5x²) B) y =ev

Q: for every choice of the constant c, the function x =( K ) / ( 1+ce−rt ) is a solution of the…

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Q: Another equation that has been used to model population growth is the Gompertz15 equation dydt=ry…

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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: 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: 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: The following shows Bisola's work in solving the equation. What is Bisola's error, any? if Step 1:…

A: Solve the equation.     253x+15=5

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: where y = 0.5772156 Show that I' (1)-log py+log p HI = L{log x; p) Р р is Euler's constant.

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

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Q: X-y 19. If log 3 (logx + logy), show that x+y = 11r %3D

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Q: 6. h(t)=- 2-1 7. g(x)%= 1-Vx-2 8. f(x) tanx 9. (x) = log(1-2x) 10. y (1-x

A: Please check step 2 for the solution.!

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

A:

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: To evaluate the integral +logx) dx we use the substitution O a. -t O b. (1+logx )²=t O c. (1+Jogx)=t…

A: Please see step 2 for answer

Q: | 1-x² y = log10 2- 5x

A:

Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: 6log3(t + 4) = 36 %3D log3(t + 4) = %3D t = II

A:

Q: y = (1 – x³)(log2x)(cot²x)

A:

Q: Q4. Find the real root using Regula Falsi method correct to 3 decimal places of the following x…

A: f(x)=x log₁₀ x -1.2 f(0)=0-1.2=-1.2 f(1)=1 log₁₀1-1.2=-1.2 (-ve) f(2)= 2 log₁₀2-1.2=-0.59794 (-ve)…

Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

Q: Determine if the given functions are LI or LD by computing the Wronskian : -2x Yi = e*,y2 = e*,y; =…

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Q: write the logarithmic equations in exponential form.

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

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: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

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: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: dy Find by first using algebraic properties of the natural logarithm dx (x+ 4)(x + 5)° In function…

A:

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: if võ zo, JT = 1 and Jū= 2 estimate Vo by constructing Logrange pelynemial, then with the exact…

A:

Q: The bacteria in a certain culture increase according to dN/dt = 0.25N. If originally N = 200, find N…

A: Integrate the equation.

Q: d.) In (z+9)– In z = 1 2 log Vx? + 21x = 3 e.) In(x+1) c.) In (x –1) = 2

A: (d) To Find: The value of x. Given: The equation is ln x+9-ln x=1. Formula used: ln a-ln b=ln ab If…

Q: calculate the integral.

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Q: 1. Which of the following functions grow faster than e* as x→∞? Which grow at the same rate as e"?…

A: Dear students,  Please find the solutions of 3 parts. In case you need help with the other questions…

Q: A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)“ , wherez…

A:

Q: 4.) Find y': Given:y = x²(3 cosh x - 1) 5.) Find y': Given: y = log, csc h (6x³)

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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: The total number of reported cases of an illness in a large city days after the start of an outbreak…

A: According to the given information the total number of reported cases of an illness in a large city…

Q: dy by first using algebraic properties of the natural logarithm dx Find (x + 6)(x + 8)* (x +3)*(x +…

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Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: Differentiate the following functions f(t) = ln | cos(ln t)| f(x) = log2 (x10ex) y = ln(( etan…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

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Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 - j4 3. 0.6 + j0.8 II.…

A: Dear Student, you have asked multiple questions, as per our policy your first question will be…

Q: 4. y = log v2x + 55. y = In(2x + 1)*6. f(x) = In(x +3)* %3D

A: topic - derivative of a function