x2 + 1)' 3/2 from x = 3 to x = 9

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

A:

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

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Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

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Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: find integral tan 5 x sec 7 x dx

A:

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: 2 9) -sinh? -cosh -dz

A:

Q: Prove 9 coshx – 5 sinhx = 15

A: This is hyperbolic function equation so we want to find x value by thi equation so. firstly, we…

Q: Solve the integral. 6х — 3 1.5 -dx 4x2 – 4x + 1

A:

Q: 2. Write closed Newton-Cotes formula with error for n=1, 2, 3 and then solve integral S* sin(x) dx…

A: The Newton cotes formulas are closed when the endpoint of the closed interval is used as a node. The…

Q: 17 0 in QII 32. sec0= - mot 15

A: Given:secθ=-1715,  θ in quadrant 2

Q: aie of sin(4x)+8 cos(x)+2x2 cos(4x)+8x sin(4x)+.

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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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 all solutions of 4sin^2xtanx−tanx= 0 that are in the interval [0,2π)

A: Given the equation  4sin2xtanx-tanx=0. We need to find the solution in the interval [0,2π)

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: 3. sin(3x) = 3s in x – 4sin³ x

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Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: */16 etan(1r) sec2(4x) dr

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Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

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

A: We have to find the value of integral

Q: 1-tanh² x sinh(2x) O cosh(2x) O sech(2x) O csch(2x) O Leave Question O |

A: To compute1+tanh2x1-tanh2x

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: 9. Solve tan x for x where 0<x<90* V3 Enter your next step here

A: Just observe that its value of tan(30°).

Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: 1. Integral of x sin^3 (x^2) 2. Integral of sin^4 3x

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Q: alue of x to

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Q: 3. In (cose) tane de

A:

Q: 2. One side of a right triangle is known to be 150 cm long and the adjacent angle is measured as…

A: The given problem is to find the maximum possible error in area of triangle when one side and angle…

Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

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Q: sec 1.)S Intanßtanß dß

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Q: cosh(3i)is equal to O -cos3 O cosh 3 cos 3 O sin 3

A:

Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

A:

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

A:

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx

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.