1.1 Find all the points on the curve x²y² + xy = 2 dy if y = x sin() dx 1.2 Find

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

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Q: Find y in terms of x. dy dx 5x 3/4, curve passes through (1, 10) A) y =- 7/4 א. -714. 5 By = 5x 1/4…

A: The given differential equation is dydx=5x-34. It is given that the curve passes through the point…

Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

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Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

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Q: 1. a) Find dy for the equation 4x²y ² - x ³y = 3 dx b) find the x-coordinate of each point on the…

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: Find y in terms of x. dy dx 12x(3x 2 - 1)3, curve passes through (1, -3) A y= (3x 2.1) 4 B y = (3x 2…

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Q: Evaluate dy/dx if y = (sec2x - tan2x)/(2cos2x-1)

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Q: 2. sin 10x , sin 20x , sin 30x

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Q: Find y in terms of x. dy aY = x 4(x 5 - 3) 2, curve passes through (1, 5) dx 17 (A y = (x5- 3) 3 +…

A: Consider a given differential equation isdydx=x4x5-32.The curve passes through the point 1,5.Express…

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.