4 the normal to the curve y= Be pont C3,4) makes cn makes an 'angle positive x- axis, what s (3)7

Q: The length of the curve y= is equal to x =3: from to 을(x2 + 2) O a. 12 Ob. 1 O c.9 Od. 3

A: We can use the application of integration in order to solve the given problem.

Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: ****- # PANKK 245 w (0 6**) jead 243 www. (**) 4 Find the length of the curve

A:

Q: Q3) Find the local maximum and minimum points of the following curve: y = 3x + 2x? - 4x + 2

A:

Q: b. The y' of the curve y 4 Vx

A: The given function is y=4x. Obtain the first derivative as follows. y'=ddx4x=ddx4 x-12=4…

Q: Find the point(s) of intersection of the curves r = 10 and r = 20 cos e. O A. (10,5) 3 OB.…

A: Given: r = 4  r = 20 cos θ

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: If y=f(x) be the curve that lies on the xy plane, then its length from x=a to x=b is given by…

Q: Q1)a) Find line that are tangent the curve x + xy = 1 at the point (-1,0)

A: The given equation of the curve is x2+xy=1 and the point is (-1, 0). Evaluate the slope of the…

Q: 3 Part 2 lateral DEFG shown below. DEFG is reflected over the line y = -x to teral D'E'F'G" Which of…

A: Given: DEFG is a quadrilateral. The objective is to find the reflected quadrilateral D'E'F'G' over…

Q: Q4:a) find the equation of the tangent and normal line to the curve y = 10 - at point (6,4). ? 7-x…

A: (a) Given curve y2=10-67-x  The equation of tangent to the curve at point x1, y1, y-y1=dydxx1,y1x-x1…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(a² + y?)' = 25 (æ² – y²) at the…

A: The given equation of the curve: 2x2+y22=25x2-y2

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.