V3 Find cosh 0, tanh 0, coth 0. 2 B) If sinh 0 =

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: Recall that cos™ 1 x = arccos x. Find r1/2 a sin(cos a) d. 1

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Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: 2. Evaluate J dx (cos³x sin³x)

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Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: a) Given that y= sinh'(cos(x)), provide detailed derivation to obtain the expression of dx

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Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: sin(4(t – w)) y(w) du = 9t?.

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x&gt;0

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

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Q: X- A coshx + B in ha +13 Sin be +4e

A: Answer

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: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: rin 2 cosh x dx. Vsinh? r + 4 sinh r + 2

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Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Find the si0pe of the given Function 1.) hlx) = sin x cos 3x at * = 3 メ 2.) y= In at メ = -2 メー! 3.)…

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Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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

Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: etany) dy cos?(y)

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Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

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Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: ∫sin^6 y cos^4 y dy, limits from 0 to pi/2

A: Consider the definite integral ∫0π/2sin6y cos4y dy to solve this integral, use the below reduction…

Q: at (x = })? dy Csc(3x) Sin(3x) + Cos(x), Find Let y =

A: The given function is: y=csc(3x)sin(3x)+cos(x)  =csc2(3x)+cos(x) To find the derivative of it:…

Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de Keep at least 2 decimal places accuracy…

A: Given that: ∫14cosxxdx and n=4

Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: Given: = 0 – sin 0; y=1– cose Find: dz2

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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: a sin a + In v ) da + tan adv = 0 Cos a

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Q: (b) If y = sin (m sinhx), find the value of (yn)o ·

A: Given   it has to find nth derivative at .

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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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.