Write the definitions of the hyperbolic functions , sinh  x  ,cosh x , tanhx

Q: Find the limit of the trigonometric function.

A:

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

Q: secA + tanA is equal to

A: Given:  To Find: To simplify the given expression.

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: Find def differenti81 equation of %3D Siny

A:

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2 x = 1.

A:

Q: Find the tangent of ZE. G 28 45 53 Write your answer as an integer or as a decimal roun tan (E) =…

A: The tangent of an angle is given by the formula- tan x=Perpendicular/ Base Now, in the given figure…

Q: tan(t) Simplify sec(t) – cos(t) to a single trig function.

A:

Q: Write sinh(x) + 4 cosh(x) in terms of e and e

A: Given: 9sinhx+4coshx   -1 The objective is to write 9sinhx+4coshx in terms of ex and e-x. Since,…

Q: find the derivatice of y=sqrt[sin(x^4-1)]

A: Consider the given equation

Q: Define the Arcsine and Arccosine Functions?

A:

Q: Use the Intermediate Value Theorem to show there is a root of the equation tan(x)=x in the interval…

A: Intermediate value theorem : Suppose that f is continuous on the closed interval [a, b] and let N be…

Q: Write in sin (arccos(3x)) with x in [0, 1/3] as an algebraic expression in x.

A: We have to find sin (arccos(3x)) with x in [0, 1/3] as an algebraic expression in x.

Q: In the given question, verify the identity:- sinh(x + y) = sinh x cosh y + cosh x sinh y

A: Consider the provided identity, sinhx+y=sinhx coshy+coshx sinhy Verify the provided identity.…

Q: Find the tangent of ZE. F 56 65 Write your answer as an integer or as a decimal rounded to the…

A:

Q: S sec4e tan30 de

A:

Q: Coshx G= sinh() %3D

A: Consider the provided function, Gx=sinhxcoshx Differentiate the following hyperbolic function.…

Q: In the given question, verify the identity:- cosh x - sinh x =- e-x

A: As we know that the hyperbolic function of the inverse trigonometric identity is given by as…

Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: Compute / / sin(x²) !! dr dy.

A: The double integrals can be solved by solving the inner integral first followed by the outer…

Q: +(x)=sin' (tan 3x) 1-

A: Since you have posted multiple questions, as per our policy we will answer first question. please…

Q: Show that coth z = }ln (). What is the domain?

A: Here we will show that coth-1x=12lnx+1x-1 and we will damain,

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: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2x = 1.

A: To show that cosh2x - sinh2x =1.

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: Determine the values of the other functions given that tanθ= 4/11, θ not included in the first…

A: Given that: tanθ=411 and θ not included in first quadrant.

Q: Find the derivative of sec−¹(x). Write the answer without any trigonometric functions.

A: You must have the idea of differentiation of trigonometric functions.

Q: 6) sin e

A:

Q: Simplify tan(t)cot(t) to a single trig function or constant with no fraction

A: To Simplify tan(t)cot(t) to a single trig function or constant with no fraction

Q: )サー cos( sinx)

A: It is given that the function fx=cos-1sinx. The given function is of the form fgx, by using the…

Q: Calculate the missing value. Use the Pythagorean Theorem!

A:

Q: Use the addition formulas for tangent to simplify the expression. [tan(e + 77)][tan(0 – 77)] + 1

A: Explanation of the solution is given below...

Q: Is  the sine function continuous every where?

A: we know that sine function is continuous on it's domain which we can see by graph of sine function…

Q: . Find the analytic function, whose real part is sin 2x/(cosh 2y- cos 2x).

A:

Q: Let f(x) = sinh x, where sinh x = %3D Find f"(x).

A:

Q: plot these functions using sub plot : x1=siny cosy , x2=secy siny, x3=sin(y-0.5) cosy , x4=…

A: Graph of function  1

Q: 9= Xsin 2x cot

A: Given function is: y = x sin^(-1) 2x + (1/2) cot^(-1) (sqrt x) Let us consider, A(x) = x sin^(-1) 2x…

Q: Derive the formula Cosh x

A:

Q: g'(θ) at θ = π/3 if g(θ) = θsinθ

A: Given: g(θ) = θsinθ      , θ= π3

Q: Find the Valve of నలాకె Sin

A:

Q: Can we use the same techniques to find the derivatives of the other three inverse trigonometric…

A: here we have to use the same techniques to find the derivatives of the other three inverse…

Q: Sketch this Functions using mathematica or any Softwape 1-1. ( LEA Sin 2. 2. 21,=4I, (SinB

A: We have to sketch the functions                                                      1.…

Q: Write the expression y tan (arccos ()) algebraic function without any trigonometric as an or inverse…

A:

Q: Sin

A:

Q: 1. Differentiate each function by using formulas. t cost (b) у %3D COSX (a) f(x) = 1+sinx

A:

Q: (a) Use S(f) to estimate |sin e" dr.

A:

Q: find the algebra  expression of the inverse of hyperbolic functions: cosine and tangent

A: Recall the fact that the hyperbolic functions of cosine and tangent is given as follows:…

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.