eik(x'-x) dk . 8 (x' – a) =

Q: Integrate 1/(1+x(1/2)) dx

A: Consider the given integral ∫11+xdx. Integrate the given integral with respect to x as follows.…

Q: Solve y'(2.5) given y = x^3 - x for h = 0.05, h = 0.01 using: a. forward diffference b. central…

A: To solve the problem we first write the formula of approximating derivative by forward difference,…

Q: (1-3/x)dx =

A:

Q: Differentiate f(x) = (3x)n() for r > 0. %3D

A: To differentiate (variable)(variable) ,  we need to take logarithm both the side then to…

Q: e* + sin x = 2/xy , find y' %3D

A:

Q: For the following systems of differential equations, (i) Find the general solution (ii) Plot the…

A: given X'=1011X (a) to calculate the general solution

Q: find y ' and  y" y = ln x /x 2

A:

Q: y = ln(7x2 + 5y2) find y'

A: We have to differentiate the given function: y=ln7x2+5y2 We will use following formulae:…

Q: 55dx 4 Stant x dx

A: Let's solve both the integrals using substitution method. We need a trigonometric identity also…

Q: / x(8x + 9)" dx %3D

A: Using Liate's rule for integration we can solve the above problem. This is also known as the…

Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: f fo=2x and g)= x-4. what is the value of rCg(3))?

A: f(x)=2x and g(x)=x-4

Q: Answer y = ce-((lnx)^2)/2

A: Given differential equation is,

Q: For the function f(x) = , find f'(x). 4x 7-x' f (x) = Answer: %3D

A: The given function is: fx=4x7-x      .....(1) To find the value of f-1x

Q: 81 xp xV In(x)

A:

Q: |(x'-x)dx=-

A: First I have split the integral in two parts, then by rule of integration find the solution.

Q: The value of (i)' is = ... O T/2 O T/2 O e^(-T/2) O e^(Tt/2)

A:

Q: y = (In x)*

A:

Q: Find y1 y=(ln x)-1

A:

Q: 1 1 400-5 .b = W = span 12 18 12 18 (a) Find the projection vector p onto W of b; i.e. p =projw(b).…

A:

Q: Estimate f'(5) of the function f (x)= 5ln(x). %3D O a. 1 O b. 0 О с. 5 O d. Ins 1 O e. In5

A: Given function is f(x) = 5ln(x) To find : f'(5)

Q: dy/dx = 6x^5sqrt(y-1) equals to y = [(1/2)(x^6+c)]^2 + 1? Diff eqn.

A: ∫tndt=tn+1n+1+cgiven  dydx=6x5y-1          dyy-1=6x5dxintegrate both sides

Q: Solve  (dy/dx) = (y/x)

A: By  variable -separable  method  we separate the variable

Q: y" +y- tanx An 8.

A: Given

Q: Find:  ∫5-9x/ (x-1)(3x-2) dx  where x > 1.

A:

Q: 1. Find the following limit lim (x,y) →(0,0) 1-cos(2x² + 2y²) x² + y²

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.