2.2 each. Solve the following inequations and sketch the region in the plane defined by (a) (b) [x]² + [y]² ≥2. [x]² - [y]² ≤ -1. [7] [7]
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![2.2
each.
Solve the following inequations and sketch the region in the plane defined by
(a)
(b)
[x]² + [y]² ≥2.
[x]² - [y]² ≤ -1.
[7]
[7]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffaf5ed0f-7da5-4d25-9b3c-65d2034b9a52%2F6b9f4bd3-6ba8-47b0-8f17-65513a59cb7c%2Fqsgkeo1_processed.png&w=3840&q=75)
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- Consider the region bounded by the parabolas x = 8y^2 and x = 5 + 3y^2.Suppose that 0< c < π/2 . For what value of is thearea of the region enclosed by the curves y= cos x,y= cos (x -c), and x=0 equal to the area of the regionenclosed by the curves y= cos(x- c) , x =π , and y=0 ?Sketch the region enclosed by the curves y = x2- 4 and y = 3x − 4, and find itsarea.
- Consider the graph of the cubicy = x(x - a)(x - b), where 0 < a < b. Verify that the graphbounds a region above the x-axis, for 0 < x < a, and bounds aregion below the x-axis, for a < x < b. What is the relationshipbetween a and b if the areas of these two regions are equal?What is the region bounded by the curves y=√x, x = 4, and the x-axis.Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.
- 11. Find the area of the region between the parabola y = 1 - x^2 and the line y = 1 -x. A. 1/6 B. 1/4 C. 1/8 D. 1/2Find the area of the region enclosed by the curves f (x) = 4x + 15 and g(x) = 2x + 33, and the lines x = 6 and x = 12.(Note that an area cannot be negative, and in this problem, neither will it be zero.)1)Find the area bounded by the given curves. a)y = 3x2 − 12 and y = 0 b)y = x2 − 2 and y = 10 − 11x2
- The lower, upper limit in the evaluation of the area of the region bounded by the two curves y=x2y=x2 and y=10x−16y=10x−16 respectively are ........... . Choose correct answer : A) x=2 and x=8 B) x=2 and x= −8 C) x=− 2 and x=8 D) x= −2 and x= −8Suppose that 0 < c < pie /2 . For what value of c is thearea of the region enclosed by the curves y = cos x , y = cos ( x-c), and x = 0 equal to the area of the regionenclosed by the curves y = cos ( x- c ) ,x = pie , andy = 0 ?Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| andy = 0 into two regions of equal area.