1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

Q: 1-In (-) + In(2x³) = In3 2- 4 log 2 – log3 + log16 = x 3-Expand In [x? sin3 x /Vx2 +1]

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Q: 5. Evalvate the Intgral S2 cos (2x) - Sin 2x)=

A: To evaluate the integral: ∫2cos22x·sin22x dx Solution: We know that, 1). 2sinθ cosθ=sin2θ 2).…

Q: Find where ln((1+z)/(1-z)) is not analytic.

A: To find: The region where the function ln(1+z)(1-z)), where z∈ℂ is not Analytic.

Q: 2. Write closed Newton-Cotes formula with error for n=1, 2, 3 and then solve integral S* sin(x) dx…

A: The Newton cotes formulas are closed when the endpoint of the closed interval is used as a node. The…

Q: 11. Use definite integrals to show that f(x) = x² – 3 and g(x) = 5 – x² have the same arc length on…

A:

Q: One solution of a 2nd order homogenous LDE is e2*sinx. What is its general solution?

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: In 1934, the Austrian biologist Ludwig von Bertalanffy derived andpublished the von Bertalanffy…

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Q: show complete solution

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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: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: sin(1+In(2x))-/1+ln(2x)

A:

Q: 1. Determine if the infinite integral is convergent or divergent dx x² + 2 - 2

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost the other…

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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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: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: dr 3. Verify that = ln(2). x(x+1) 1

A: Given: ∫1∞dxxx+1=ln2

Q: The approximation of the root x* of the function f(x) = -x + sin x - 1 accurate to within 10-³ using…

A:

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: Find the indefinite integral. [ cos 3xar sin33- sin 3r +C 6. O sna(3- sn'ax) sin3 3-sn 3 +C sn3x…

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Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

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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: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: The graphs of y = 1/x and y = 1/ln(x) are shown at right. 2.0 15 a) Set up fully, but do not…

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Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: The approximation of the root x of the function f(x) = -x + sinx-2 accurate to within 103 using…

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Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

A:

Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

A:

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: Use the methods of differentials to estimate the value of (x+1) over the square root of 2x+1 at…

A: Use the quotient rule to find the derivative for f(x).

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: Prove that the arc y = log secx from les (2+ 3

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Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

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Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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

A: We have here g(x)=(13)(1+cos(x)) fix point iteration formula is xn=g(xn-1) we are given x0=0

Q: cos(9x) -dx COS J 1+ sin²(9x)

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Q: Evaluate /(e* + - + cos4x)dx O + logx + sn3x +c e2r 3 4 e3x sin4x + logx + + c 3 2 O + logx + e5x 2…

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Q: 11 Show that Simpson's rule withn=2 (so there are 2n = 4 subintervals) gives the exact value of (2x…

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Q: Find differential o perator theit annihilates 4e cos3x+3x2e

A: Given that: 4e2xcos3x+3x2e5x For the differential operator that annihilates the value of f(X) will…

Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.