Evaluate the function (a) sinh−1 0 (b) tanh−1 0 . If the value is not a rational number, round your answer to three decimal places.

Q: Find the indefinite integral: cos ( πx ) dx sin, ( π )

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Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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Q: Find the indefinite integral ∫sin5 x dx

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Q: differentiate the given function 4. f(w)= sin(w)+ w* tan' (w) solve it on paper

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Q: Evaluate the definite integral 8 sin(x)dx

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Q: Which of the following functions is/are TRUE? A sinh(-x) = -sinhx B cosh(-x) = coshx tanh(-x) = -…

A: topic- hyperbolic functions we know that sinh(-x)=-sinh(x) cosh(-x)=cosh(x) tanh(-x)=-tanh(x)

Q: Show that y = tanh x is an odd function.

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Q: 6. Use the Successive Approximation method to find correct to four significant figures a real root…

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Q: Find the derivative of the functions. (Answer Five only ) xIne 1- y = In x 2 In 5 In 25 2- y =…

A: In this question we have to find the derivative of the functionwe

Q: 18. sin y cos"ydy

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Q: Show that y = tanhx is an odd function.

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Q: (a) Find the derivative of the function g (x) sin? x + cos? x (b) then use a trigonometric identity…

A: a) Given function: gx=sin2x+cos2x

Q: FInd the intervals in which the function f(x) =sin(logex) +cos(logex) is decreasing

A: Given function is, f(x)=sin(logex)+cos(logex)

Q: Q2: find the integral of trigonometric function cos sint dx

A: To evaluate the integral: I=∫0πcos5x sin4x dx⇒I=∫0πcos4x sin4x  cos x dx⇒I=∫0πcos2x2 sin4x  cos x…

Q: . h(x)= cot 1 -tanx

A: Given:hx=cot-11x-tan-1x

Q: Accurate to 5 decimal places and in 0% approximate error, find the root of f(x) = sin x - 1/3 x, in…

A: Newton Raphson method

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Find the indefinite integral ∫π sin πx dx

A: we have to find the integral ∫πsinπxdx

Q: 2. Differentiate the following functions, simplifying your answers where possible. (a) In(2*) (b)…

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Q: Evaluate the indefinite integral. | = sin(x) cos(4x) dx +C

A: Given query is to find the intersection.

Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: Find that antiderivative of tan° x whose value at x = 0 is 1. O is

A: Given that: tan3x

Q: S", sin x dx

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Q: Evaluate the definite integral ,x°dx. Afterward, sketch a graph of y = x³ and use it to give a…

A: Given,  ∫-21x3dx  We have to evaluate the definite integral and sketch  a graph of  y = x3 to give…

Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, X3- f(x) = 1 – 5x sin(x), xo…

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Q: Evaluate the integral.

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Q: Breathing is cyclic, and a full respiratory cycle from the beginning of inhalation to the end of…

A: Given ft=710sin2πt3 to find vt

Q: Use reduction formula to find (tanh" xdx 10

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Q: Accurate to 5 decimal places and in 0% approximate error, find the root of f(x) = sin x - 1/3 x, in…

A: The given function is fx=sinx-13x in the interval 2,2.5. Calculate the Accurate to 5 decimal places…

Q: Find the indefinite integral ∫tan5 (x/2) dx

A: It is given that, ∫tan5x2dx. We have to evaluate it.

Q: Use the Newton-Raphson Method to approximate the root of f(x) = 2 cos(x) – 2x + 1.

A: Newton Raphson method: numarical methods

Q: T/6 sec² xdx 1+9 tan? x

A: Given query is to find the value of the integral.

Q: 18 sin a dx

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Q: 3. Evaluate tan¹x² 1+x dx.

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Q: Evaluate the function (a) sinh 3 (b) tanh(−2).     If the value is not a rational number, round your…

A: a). sinh3=e3-e-32     ∵sinhx=ex-e-x2=10.0178≈10.018

Q: Use the Secant Method to approximate the positive root of 2x^2-sin^-1x=0. Sketch the graph of the…

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Q: evaluate the definite integral from 0 to (1/3) of pi*tan(pi*x)dx

A: Given expression is,

Q: X sin x x dx 4+ x ーa/2 :-

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Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: 6. S(x)= In(tanh 5"

A: As per bartleby guidelines we only give first question answers.

Q: Differentiate the function.

A: Consider the following equation: y=e-2tcos4t Differentiate y with respect to t: dydt=ddte-2tcos4t…

Q: 8. x sin-1x dx

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Q: | sec* x tan x dx

A: Given integral is ∫π4π2sec4x tanx dx

Q: (a) Express () n lim > sin - n i=1 as a definite integral.

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Q: (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that…

A: The solution is given as

Q: 00 e-st cosh t dt

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Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: Calculate for one real root of tan r = 4x with xo = 1.2 up to four decimal places %3D using the…

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Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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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.