Find Sn{sinh(x)} = %3D O A. Lnn(-1)" sinh(L) L2+n2n2 O B. None O C. Lnt(1-(-1)" cosh(L)) L² +n²n² O D. L2(-1)" sinh(L) L² +n²n² O E. L²((-1)" cosh(L)-1) L2+n2n2

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the…

A: Given initial population = 120  So, for t=0, P=120  Using that we get: Quadruples in size every 1.5…

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

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

Q: .3 X ナメ-2 find x using fixed point method where X= 015 (initial Value)

A: The given function fx=x3+4x-2 Find the value of fx at x=0.5. f0.5=0.53+40.5-2=0.125>0 Find the…

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: 8. Find the principal value of Arc tanh(1 + j2)

A:

Q: A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3…

A:

Q: A virus spreading across the country is making people sick. Let x be the number of infected people.…

A: If x be the number of infected people. Then it is given that DE is proportional to the infected…

Q: Compute sinh(ln 5) and tanh(3 ln 5) without using a calculator.

A:

Q: 5. A capacitor has a capacitive reactance of 50 2 when connected to a 60-Hz line. What will be the…

A: Consider the provide question, Hello. Since your question has multiple parts, we will solve first…

Q: Find an approximate value for x (to 2 decimal places) if 5=(3lnx) - (lnx/2) . Find y'' if y =…

A:

Q: Suppose that you now have $10,000 and that you expect to save an additional $4000 during each year,…

A: Given that, you now have $10,000 and that you expect to save an additional $4000 during each year,…

Q: Solve 4 sin 2x S1₁= 8 4 -1 -¹x³ + x²-x² +2 dx

A:

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

A:

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

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

Q: 2. Find a real root of 3x – logi0 x – 8 using the Successive Approximation method. Correct to four…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

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

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: An angle Θ is known to vary periodically with time, in such a way that its rate of change is…

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Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

A:

Q: tion of the differe = e-x + x2 is

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Q: logtan nx(2+ 4 cos nx) 2

A:

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

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: 3- Find dy/dx for y = log2(1- sin (3x2) %3D

A:

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(1 − 2x) dx

A:

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Step 2 Solve the new integral using the General Log Rule. Then, back-substitute x into the equation.…

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Q: Integral sinh2xcosh3xdx

A:

Q: If x and y are measurements of certain parts of an organism, then the rate of change of y with…

A: Formula used: The differential equation can be equivalently expressed in the form g(y) dy=f(x)dx…

Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: How is ln x affected if x is multiplied by et?

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Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

A:

Q: se limit methods to determine which of the two given functions grows faster, or state that they have…

A: Let f(x) = ex2 , g(x) = e10xIf limx→∞f(x)g(x)=∞ , then f(x) grows faster than g(x)If…

Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

Q: Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional…

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

A:

Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 3 cm3…

A:

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.