2. Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross. Between y = x - 5x + 3 and y = -x + 5x – 5 for x in (0, 4].

Q: 11. Find the area of the region bounded byy = (x - 1)² + 1, the x -axis, x = -1, and x = 2. A. -6 C.…

A: Here we are using integration method to find the area of the given region.

Q: ニ1 近。 Question 2 D. O E OA 3. (A) 3. 3. (). 32 3. (C) 16. (B) zg (7) The area of the region enclosed…

A:

Q: #1 Find the area of the region between y=2x+ and y=x=4

A:

Q: Find the area of the region bounded by the graph ofy =1/x the x-axis, and the vertical lines x = 1…

A: The area is calculated by taking a rectangular element of width  dx and height y. The total area is…

Q: B- Find the area between the curves: x = y2 and y = x - 2

A:

Q: 1. Find the area of the region bounded by the parabola x = 3 + 2y – y? and the line 2x + 3y = 6.

A:

Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: of the region in the first quadrant that is boun d below by the x-axis and the line y=x-2

A:

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

A:

Q: Find the area between the y-axis and the graph X = Y 7 6 5 4 X 543-2/1² 1 2 3 4 5 WŃ y - 1 on the…

A: Here we have to use the concept of integration

Q: 3. Find the first quadrant area bounded by the following curves: y = x² +2, y = 4 and x = 0.

A:

Q: I- Find the area of the region bounded from the right by the curve x 4-y, from the left by the line…

A:

Q: 9. Find in two ways the area bounded by the parabola y = x², the y-axis, and the lines y = 1, y= 4.

A: Given,  The parabola y = x2  We have to find the area bounded by the parabola, y-axis and the lines…

Q: 9. What is the area of the largest rectangle that can be drawn with one side along the x-axis and…

A: Consider the provided information, Now, draw the figure of the provided information.

Q: 10. Find the area of the region bounded by the graph of x = y² – 4y – 5 and the y-axis.

A:

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: 3) Find the area of the region enclosed by the following line and the curve. y = x – 1 and y² = 4x +…

A: The graph for the given functions y=x-1 and y2=4x+1 is shown below.

Q: (4) Find the area of the region in the first quadrant bounded above by y = √x - 1 and y = x - 3.

A:

Q: Which of the following gives the area of the region between the graphs of y = |x| and y = 7

A:

Q: Question 23 What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-4?

A: It is required to find the area made by curve between x axis and the given points.

Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: Area of the region under the graphs? Integral related question

A:

Q: Q. 1. Find the area of the region enclosed by the parabola y = 3 – x² and the line y = -2x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the area between the following curves: y=x^2-30 and y= 10 - 3x

A: To Find the area between the following curves: y=x^2-30 and y= 10 - 3x

Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: 2. Find the area between the curves. x = - 2, x = 1, y = 6x, y = x2 - 7

A: Given: x=-2,x=1,y=6x,y=x2-7

Q: (1) Find the area of the region bounded by the curves and draw an illustration y = x² and y = 6x-x².

A: The region bounded by the curves y=x2 and y=6x-x2 Note:    Multiple questions are given we are…

Q: Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the…

A: Solve by using the concept of maximizing any term

Q: 1. Find the area of the regions shaded by the following curves: r = 2cos0 and r = 2sine

A: Formula: The area of region between the origin and the curve r = f(θ) α ≤ θ ≤ β is given by A =…

Q: 5 m 4m 4 m 3 m 3 m Find the area of the region bounded by the graphs of y2 = 4x and the line 2x - y…

A:

Q: 10. y = x; y = x'; x+ y = 2

A: Function is the unique relation, where each x is mapped to unique y. It can be of many type,…

Q: 1 2. Find the total area of the region between the curve and the x-axis. a. y=2-x; b. y= 3x-3;…

A:

Q: 4. Find the area between the curves y = x2(x – 3) and y2 + 8y – 16x + 48 = 0

A:

Q: Find the area of the region enclosed by the given curves. y = 13-x2, y=x2-5

A:

Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: 1. AY -x² +1 y=x

A: we have to find out

Q: 1)Find the area of the region bounded by the given curves and lines for the following problems:- V…

A:

Q: For what values of m do the line y = mx and the curve y = x/(x² + 1) enclose a region? Find the area…

A:

Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

A:

Q: 7) Find the area of the region enclusced by the curves y=x² and

A: Please refer the attached image for complete solution. THANK YOU !

Q: Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the…

A: The given question can be solved as shown in step 2.

Q: Find the enclosed area by the curve with equation y = x² - 9 and the X-axis in the region [−1, 2] 24…

A: In this question, we want to evaluate the area of the region enclosed by the curves y=x2-9 and X-…

Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

A:

Q: )Find the area of the region bounded by the given curves and lines for the following problems:- 1.…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 5. Find the area bounded by the parabola y = x^2 - 3 and the line y =1.

A: Given problem:- Find the area bounded by the parabola y = x2 - 3 and the line y = 1 .

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

A: The solution are next step

Q: 7. Determine the area to the right of g(y) = y² + 2y – 4 and to the left of the line x = -1.

A: By using area between the curve formula, We calculate the required area.

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.