Verify Eq. (2): cosh2 x - sinh2 x = l.

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Q: Estimate the root of 2 cosh x sin x 1, using the secant method, with an accuracy of 4dp. Take 0.4…

A: Image is attached with detailed solution.

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (2…

A: Given function is   Differentiating both sides with respect to x, we get

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: What is the nth derivative of eb? 3ekx? y%3D ekt O ekr k"ekt O kekr

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Q: L(cos(at)sinh(at))

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Q: • y= cos(a' + x')

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Q: What is the derivative of: y = arcsin(cos x2)

A: Our Aim is to calculate the derivative of y=sin-1cos x2-(i)

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Q: Solve for the derivative Arc sin + Arc cos =0 y y

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Q: b) Differentiate (Cosx)Stnx with respect to (Tanx)Secx

A: We have to differentiate cos xsin x with respect to tan xsec x

Q: sinh(In In a)da is equal to xlnx

A: To find:∫sinhlnlnxxlnx dx

Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: Which is the derivative (dy/dx) of y=sin-1 tanx?

A: Formula used   (fog)'(x) = f'(g(x))*g'(x)

Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

Q: Evaluate the integral.

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Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: Apply Newton-Raphson method to determine a root of the equation cosx- xe^x correct to three decimal…

A: Let us consider an eqaution f(x)=0 with the initial point x0 to determine the roots of the equation…

Q: Find , if y = x sinh x - cosh x %3D dx

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Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

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Q: sin“ (x)dx 4

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

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Q: Find the derivative. ( cos ft dt x10 COS^/

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Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

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Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: Solve for the derivative of y=ln ln [cos2(3x)] With the answer -6 tan tan (3x)  Show solution.

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Q: sinh 2x cosh 3xdx.

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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: Where is the function sin (log (r2 + y²)) continuous?

A: Function = Sinlogx2+ y2

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Which formula gives the x-coordinates of the maximum values for y = cos(x)?

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Q: Using integration, derive the La L(sinh at)

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Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: Find the second derivative y=lnx + 3 sin(4x) d²y dx² of

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Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

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Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: Find all extreme values for y=x+sinx^2 over [0,π]

A: Given,  y = x + sin2x  We have to find the extreme value in the interval 0, π

Q: 14. y = In cos 4x

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

Q: Find the root using newton raphson method for f(x) = sin(x) − x²

A: Given function is f(x)=sin(x)-x2 From the given equation, it is clear that 0 is one of the root of…

Q: ind the second derivative in its simplified form 2. y= 4 Arccos x/2 +2 square root of 4-x^2

A: Given, y=4arccosx2+24-x2

Q: What is the derivative of y tan-1 cos 4x ?

A: By see this solution below

Q: In(x*y?) — х? +уз

A: Given equation is: lnx3y2=x2+y3 ......................... (1) We have to find d2ydx2 i.e. y".…

Q: Find the derivative of the function f(x) = x sin(6x + 14)+ In(5z+9) Answer:

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Q: Find the derivative. sint 1 du 16-u? 미행

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Q: sinh(cot(x)) x2 + 1 dx

A: To Determine: find the integration Given: we have ∫sinhcot-1xx2+1dx Explanation: we have an integral…

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

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.