* [). Find L-1 Find L-' . Find L-' [ 2s-3 7-3s+2.

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

A:

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

A:

Q: 9-x² dydx. 2

A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A:

Q: 4. Determine exact values of 0 if 0 < 0s 2n given that tano - V3. Explain your process.

A:

Q: Solve using variation OF patometert O reductian OF order CD-+)y= secx csc x csc X

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: Using Differentials, approximate (4499)2-(401)2 AM

A: To approximate: 4.9992-4.012 Let, z=fx,y=x2-y2x0=5, y0=4 For the function z=f(x, y) at the point…

Q: tion of all components of v(3) correct to two decimal places.

A:

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: In (In(ax))

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Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: he surface al derivative

A:

Q: 2. Identify the derivative (9) based on the product rule ie, (G). Simplify to a single term.

A: Given ∂∂TGT

Q: Finel for r=1-Sino

A:

Q: 1-E-, find x, y from エ+y 4. 3 3.

A: given two matrices are equal. that means, Both matrices have same order, and the corresponding…

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

A:

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

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

A:

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: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: Find the differential equations of every families of curves given. 1) All circles.

A:

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

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

A:

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

A:

Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

A:

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

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Q: Sec-S 2 1 TanOLO

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

A:

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: adient of f in diro

A: Given function is: f(x,y,z) = xy + yz2 + xz3.

Q: uxiliary equation of + by = 0 are re tion of the different

A:

Q: 4 + sinh(3x) = 4 cosh(3x).

A:

Q: Use the hyperbolic identity cosh(2x)= 2 cosh2 (x)-1 to solve 4 cosh(2x)– 22 cosh(x)+ 19 = 0 .

A:

Q: Use differentials to approximate √16.5.

A: Given:

Q: у %3DIn(In sec x)

A:

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)

Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

A:

Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x&gt;0x=-x if x&lt;0 therefore,…

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

A:

Q: Prove sech 2  x =1 - tanh  2x

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

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: sech2(In x)

A:

Q: s(w) = In( w - %3D

A:

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.