Solve Ytt = = 4yxx 0 < x < 1, t > 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    =&gt; y' = dy/dx = 3 - 3x2 = 0 (set)                =&gt; 3(1 - x2) = 0…

Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

A:

Q: f(x)= x2/5 Where it concave up/down?

A: To find the concavity of the given function.

Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

A:

Q: Solve for a) given y= 2f(x) solve for x b) given y=-3f(2x) solve for x c) given y= f^-1 (4x) solve…

A: Given Functions are as follows

Q: For f(x) = x2 - 5x + 6, find f(2), f'(2), and f(3) – f(2). a. f(2) = b. f'(2) = c. f(3) – f(2):

A: Given function is f(x)=x2-5x+6 (a) f(2) is obtained by replacing x by 2 in f(x) as follows.…

Q: Differentiate x4 - 4x + 3 - f(x) = Vx +1

A:

Q: 1) fix) = (x-2).x+1 find the maximum,minimum and inflection paints of the finction. %3D

A: An inflection point is a point at which the second derivative is equal to zero or is undefined and…

Q: Find f(x) if f' (x) = 3x – 2x + 3 and f(2) = 15. - f(z) = Preview %D

A:

Q: Decide whether 3f”(x)+20f’(x)-7f(x)=0 for f(x)=ae^r 1^x + be^r 2^x. Substitute your values for r1…

A:

Q: Find the value of the constants a and b given that F'(x)= 2ax + b, F(3)= 47, F(-2)= -3, and F(1)=3.

A: We have given F'x=2ax+b Then, integral on bothe sides we get ∫F'xdx=∫2ax+bdx Fx=ax2+bx+c where c is…

Q: Find f such that f'(x) = 5x² + 7x − 9 and f(0) = 9. f(x) =

A:

Q: Given: dyldx = (4x^2 - 7x) / (3y^2 + 2). Find the particular solution at x = 1, y = 1. %3! 6y^3 +…

A:

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5]. O f(4)=0.31,…

A:

Q: X and Y are independent. Var(X) = 6, E(Y^2 ) = 12, and E(Y ) = 2.5. Find Var(3X − 2Y − 8).

A:

Q: (2/x+1)(x– 1) Find the f'(x) of the function f(x) = x+3

A: Given, f(x) = 2x+1x-1x+3 f(x) = 2x32-2x12+x-1x+3 We know that ddxxn = nxn-1  and quotient rule of…

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.