2. Find a real root of 3x – logi0 x – 8 using the Successive Approximation method. Correct to four decimal places.

Q: Then, use a calculator to obtain a decimal approximation to three decimal places, for the solution.…

A: Given that 2log3x+4=log39+2.

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: Use the trapezoidal rule with five function values, together with appropriate log laws, to show that…

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Q: By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the…

A: Consider the integral

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

A:

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…

A:

Q: Explain what is wrong with the following statement: "“The right sum with 20 rectangles ap-…

A: We know that ∫abf(x)dx If we divide the intervals [a,b] into n equal sub-intervals…

Q: (a) Find if y(x) = log3(729) sec(In(r)) + In()r+ e

A:

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: solve: loga (4x+4)= log₂ (-7x+19) = X= AS lenter DNE if no rolution)

A: topic - logarithmic equations

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

A:

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

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: y = loga 4x 6.

A: Differentiate with respect to x.

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

A:

Q: Solve by hand function bellow using Newton method. Repeat 5 times. (5 iterations) f(x)=x® +4x2-10

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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: 1 (log, x)' 3x ise b =?

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

A:

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: Perform three iterations of Newton's Method to estimate the zero of f(x) =x4– 15x +12 with an…

A: Consider the function  fx=x4−15x+12x0=3

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

A:

Q: 10. y = log2(3x + 1) %3D

A: We have to solve

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 the absolute maximum value of ƒ(x) = x2 ln (1/x) and say where it occurs.

A: We need to find the absolute maximum value of the function

Q: Use the method of Successive Approximation to find a real root of e^x – x^2 = 0 correct to four…

A:

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: Find one real root of g(x) = ln(xª) = 0.70 between 1 and 2. How many number of iterations were…

A: Before starting the solution, let we explain the False Position Method.Intermediate value theorm: A…

Q: Use the Newton-Raphson method to find the root of sin(x) = e=x For this problem, use initial guess…

A:

Q: Q5: Evaluate : 3 1- Domain of:- log10 (x-x) 2- Rang of : cosx – sinx 3x +3y = 28y (3x+y = 27 ) %3D…

A: Domain of log(x) is x>0.

Q: 3.) Find the root of f(x) = e* -x using Newton's law of approximation.

A:

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: 6. Which of the following functions grow faster than In x as x→∞? Which grow at the same rate as In…

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Q: Find the positive root of the equation r2 - log10(T) = 12 correct upto 3 decimal places using false…

A:

Q: b. y= tan(7x-3)•log 4(5 + 2x) use the Product rule (3)

A: We use product rule of derivative :d/dx(uv)=ud/dx(v)+vd/dx(u). See 2nd step.

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

A:

Q: i. Find the real root of the given function f(x) = e²x − x − 6 = 0 by Newton-Raphson iterative…

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

A:

Q: Perform three iterations of Newton's Method to estimate the zero of f(x) = x5 – 13x +9 with an…

A: Explanation of the answer is as follows

Q: ` log x dx

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Q: d log, x = 1 dx [(In a)(x)]

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Q: What is the linear approximation of log base 5 x at x=5

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Q: Find the approximated value of x until 4 iterations for e* = 3 log(x) using Bisection Method. Show…

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Q: calculate the first four iterations for the approximate value of the root of the function f(x) =…

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Q: Eхample 33. x" log x dx .

A: