f(n) Σ? log' (2i) Derive matching upper and lower bounds for i=1 You can assume n is even.

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

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Q: ln(x) is just defined for x greater than 1. Select one: True False

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Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

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Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: Find the root of the function using Fixed-point Iteration. f (x) - x cos (x) - x?

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Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

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Q: (sin(x)²) dx Is it converges?

A: Given integral is ∫0∞sin(x)2xdx firstly we will find the simplest form of integration. We have…

Q: 10) lim TT X-- sinx-cosx - TT X- 4

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Q: Using Differentials, approximate (4499)2-(401)2 AM

A: To approximate: 4.9992-4.012 Let, z=fx,y=x2-y2x0=5, y0=4 For the function z=f(x, y) at the point…

Q: Determine whether the equation ln(x + 1) = ln x + ln 1 is true or false. Where possible, show work…

A: we have to determine whether the equation is true or false ln(x+1)=lnx+ln1

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Select a suitable technique for each indefinite integral. (Justify) Solve for each integral.

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Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

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Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Using Newton Raphson method, do 4 iterations to find a positive root for f(x)=sin(x)-x² starting…

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Q: x-1 y = log, x+1

A: We know, ddxlog(x)=1x ddxu(x)v(x)=v(x)u'(x)-u(x)v'(x)v(x)2 log(ab)=log(a)-log(b) log(a)n=n*log(a)

Q: x* +00 + 3 -dx x² + 3x + 1 -00 8

A: Note that for x>3 and x<-3, x4+3x2+3x+1>x. Now, ∫-∞∞xdx diverges so, ∫-∞∞x4+3x2+3x+1dx…

Q: The tangent line at x = 5 to the graph of f(x) = x passes through the points (5, f(5)) and (6, 200).…

A: Given, f(x)=x³ Therefore, f(5)= 5³= 125

Q: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

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Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, ƒ (x) has a root in [0, 1]. To…

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Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: logtan nx(2+ 4 cos nx) 2

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Q: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: 3) Find the second derivative of 2x f(x) = for x + 0 3x2+4x Show all steps. Simplify your answer as…

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Q: Use the mean-value Theorem to prove 1 1 - < ln(x + 1) − ln x < - X x +1

A: Consider the function f(x)=ln(x) So, f(x) is continuous on 0,∞ and f(x) is differentiable on 0,∞.…

Q: = -log₂ (x+3) y=. Equation of Asymptote: Mapping Rule: 2 0

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Q: An exponential function for which the derivative is al- ways negative.

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Q: Compute the derivative of Sin x in two ways: (i) Using the chain rule. (ii) Taking the derivative of…

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Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

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: Use differentials to approximate √16.5.

A: Given:

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

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Q: Find cosh æ In(sinh x)dx.

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Q: Find the value of x5 in 3 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: ticle at time t assuming that x(0) = -1

A: The eigen vectors are : v1=-31 , v2=-71 The eigen values are : 7 and 5. The initial condition is…

Q: How do I solve the limit as x goes to -1 for the expression (sin(3x-3))/(1-x) without using…

A: The given limit is,

Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

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Q: solution to ln x =-x+8 to three decimal places. Continue iterating until two successive

A: Please refer to the image below

Q: se limit methods to determine which of the two given functions grows faster, or state that they have…

A: Let f(x) = ex2 , g(x) = e10xIf limx→∞f(x)g(x)=∞ , then f(x) grows faster than g(x)If…

Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

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

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Q: Find the value of x5 in 1 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: calculate the integral.

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Q: Use an appropriate technique to integrate: ∫ ln(5x) dx Upper limit: e/5 Lower Limit: 1/5

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Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

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Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.