2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

Q: If k > 1, the graphs of y = sin x and y = ke¯² intersect for x > 0. Find the smallest value of k for…

A: Given that if k≥1, the graphs of y=sinx and y=ke-x intersect for x≥0. When the graphs are tangent,…

Q: 2. a) Calculate the 4th roots of (5 - j3) b) Differentiate the following functions clearly showing…

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Q: If cosh x  =5/3 and x>0 , find the values of the other hyperbolicfunctions at x .

A: Given  cosh x  =53 , x>0

Q: Find the length of the graph of y = (1/2) cosh 2xfrom x = 0 to x = ln 25.

A: Length of the graph y=f(x),a<x<b is given by L=∫ab1+dydx2dx Here,  y=12cosh 2x⇒dydx=122sinh…

Q: 5. Use implicit differentiation to find 8z and x² + 4y? + 92? = 8 %3D

A: 5. Some equations in x and y don't explicitly define y as a function of x. In such cases we do…

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

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Q: 4) Verify the identity using the definitions of hyperbolic functions. e2x + 1 e2x – 1 coth x

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Q: Find the length of the graph of y = (1/2) cosh 2x from x = 0 to x = ln sqrt(5).

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Q: Use Newton’s method to approximate, to within 10−4, the value of x that produces the point on the…

A: Given: y=1x and sme point 2,1

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

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Q: Suppose z and y are funetions of time and satisfy the formula e sin y = In y + tan dy Write a…

A: Solution:- differentiate with respect to t.

Q: 2. STO Find the length of the graph of y = 2+ In(sin z) om the interval [7/4, 7 /2].

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Q: Match each given function to one of the graphs. y= 6 sin y=6 sin y= -3 cos (8x) y=6 cos y= -6 sin y…

A: Functions  To match the given functions with the graph given below.

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: Find exact Values for x in the interval 0,360°) that satisfY the equation. 3Sin 2x+2Sinx=|+3cosX

A: Given equation 3sin2x+2sinx=1+3cosx

Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

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Q: Answer all the following 1- Find y" for y = x².tan-1x -1+cos2x 2- Find lim (by using L'hopital's…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The base of a three-dimensional figure is bound by the graph y = sin(x) + 1. Vertical cross-sections…

A: Given the base of 3-D figure is found by y = sin(x) + 1. The cross sections are vertical and…

Q: Use Newton's Method to find the two solutions of eª = 4xl to six significant figures. 12 1,0 -1…

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Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: Use linear approximations to estimate the following. 1. sin 9/4

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Q: Eliminate the parameter (4) from the following. (A =5+sint YA=2+cOst

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Q: Show that the formula gives the decomposition odd function. e* = cosh(x) + sinh(x) of the function…

A: Even function: Let fx is the real-valued function, where x is the real number, then, fx is an even…

Q: EX-16- Let tanh u = - 7/ 25 , determine the values of the remaining five hyperbolic functions.

A: Using the trigonometry hyperbolic formulas: Coth u = 1/ tanh u tanh 2 u + sech2 u = 1 Cosh u = 1/…

Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

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Q: Find the max and min values on the given interval for #3 and x+5 3. у %3 [-3,3] 16-x2 T- 4. у %3D…

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

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

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

Q: 2* csch (2*) cosh(2*)-sinh(2*)

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Q: A rectangular box is to have a square base and a volume of 20 ft. If the material for the base costs…

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Q: h) = 3 sin h (1-3x) cosh (1-3)

A: Given that hx=3sinh1-3x2cosh1-3x2 The objective is to find the derivative for h(x). The facts used…

Q: Find the extremum points for the following functions if they exis f(x) = 3x² + 2 cos(x),

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Q: Give an equation for a cosine function that has a maximum at followed immediately by another maximur…

A: To find the trigonometric equation satisgmfying the properties

Q: cosh

A: Given function is Fx=cosh1x3.

Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x3y2 sin(xy)…

A: Given below clear explanation

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

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Q: 2x csch (2*) cosh(2*)-sinh(2*)

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

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Q: 5.1 Write down the domain of the function, using set notation. 5.2 Explain why the following…

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Q: Find all roots of the function x- cos-1 --3 = 0,using Newton -Raphson Mlethod.

A: The equation f(x)=0 has a root on some interval if the equation of the graph intersect the x-axis…

Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

A: Given equation is f(x)=x2-4sin(x) Initial approximation is x0=3 Now f'(x)=2x-4cos(x) formula for…

Q: 5. (a) A company manufactures cylindrical metal drums with open tops with a volume of lcubicmeter.…

A: Given functions are y1=sinx; y2=sin-1x; y3=cosx; y4=cos-1x; y5=tanx; y6=tan-1x; y7=2+x+23; y8=x2-4;…

Q: π 5A Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= - tox=₁ 4 4 1.414…

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Q: 6. y 45

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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.