If tanh(x)=5/13, what is the sinh(x)?

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

A:

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: sinh2 (등)

A:

Q: Use Newton Raphson methods to solve X |sin(x)| = 4.1

A: Newton Raphson method: Roots of the equation f(x)=0 are given by iterative formula…

Q: EX / Show that cosh x-sinhx=1

A:

Q: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

A:

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

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: Evaluate the integral.

A:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

A:

Q: In (4e3) In2

A:

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

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: A calculator has a built-in sinh-1 x function, but no csch-1 x function. How do you evaluate csch-1…

A: Evaluate: csch-15

Q: sin(20nnt) AS(t)ln:odd = Ln=1 %3D

A: The Given problem is:…

Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: Obtain the derivative formulas for csch x, sech x, and coth x from the derivative formulas for sinh…

A: Given functions are sinhx,coshx,tanhx.

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

A: To find:∫sinhlnlnxxlnx dx

Q: y = e*In(sinh x)

A: See the details solution in below

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: Find the indefinite integral ∫sinh 6x dx

A:

Q: Find the first derivative Complete Solution.  1.) t=sinθtanθ

A:

Q: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: Find the indefinite integral ∫coshx/sinhx  dx

A:

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

A:

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: cosh(2x) = cosh?(x) + sinh² (x).

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: Q2): If sinh(x) =find tanh(4x). %3D

A:

Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: As x gets closer to zero, tan2x/ln(1+x) gets closer to what value?

A: This question can be solved using the concept of L HOSPITAL,'S RULE.

Q: 5. Explain in words what the output of sinh (y) geometrically represents. ule

A:

Q: Find the indefinite integral. ∫e−3x sin 5x dx

A: ∫e-3x sin5x dx

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

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

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

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

Q: Solve for the second derivative(y") of the following and simplify the final results. Show complete…

A: Given. ⇒4lntan-1x=1-y⇒y=1-4lntan-1x Taking derivative with respect to x, we get…

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: Find the first derivative of the function y = In[tan (pi/4 + x/2)

A:

Q: 1. sin?(ešin*t) + cos¯'(2t³ – 5)

A: Solution: ddxsin2(esin2t)+cos-1(2t3-5)

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x&gt;1 at x=10

Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

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.