1 1 8. If A= ,then A( where k is any integer number) is 0 1 [ k (a) A = 0 k 1 k (b) A = k k (c) A = (d) A = (e) none 0 1 Q9. The condition on a such that the function f(x. v) =r +2oxy +16v?is nositive semi deinite cxcent at noint

Q: C. Simplify the following Boolean expression and Implement the simplified function F. F = xy' +…

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Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: If the function f:R →R given by f(x) = x' + ax? + bx + 5sin? x is an increasing function, find the…

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Q: (x² + 2 , x² – xk – 3 , x 5 7. Find the value of K that makes the function f(x) = Continuous at x =…

A:

Q: 3. Show that f(x) = e describes a bijective function from R to (0, +∞0). (a) Show that f is a…

A:

Q: 5. Let f : R -→ R be defined by f(x) = 2x +9. Find a formula for f-1.

A: We need to find the inverse function of the real valued function f(x)=2x+9

Q: 9. For what value of the constants A and B is the function A√x+6-1 for Br² +2 f(x) = 2 Ar + B f…

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Q: Let f(x) = 36 – 5z – z?. (A) Use interval notation to indicate where f(z) is increasing. Note: Use…

A: Answers are provided below.

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

A:

Q: Let X = R – {2} and Y = R – {3}, where R is the set of real numbers. Show that Card(X) = Card(Y).…

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Q: b. Let g(x) = x² – 7. Determine the root(s) of g. 7,-7 Preview 7 = 7., – 7 = -7. c. Let h(x) 5x? -…

A: Topic = Algebra

Q: How many injective functions f: {1,2,3,4} {1,2,3,4,5} are there with f(n) < 2n? O 12 O 36 O 24 06

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Q: 2. Let m and b be rea If fis both continuo

A: Topic:- calculus

Q: Q2. Determine all values of a, b, c, d, e for which the following function is a cubic spline (a(x –…

A: Given that, fx=ax-22+bx-13    x∈(-∞,1]cx-22    x∈[1,3]dx-22+ex-33…

Q: 8. Find the domain of the following function. Show the work that leads to your conclusion. Express…

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Q: [2x – 1] lim where [2x – 1] is the greatest integer of 2x – 1 3 – |4x + 5| Which of the following…

A: Given, limx→32+2x-13-4x+5 x=32+h,  h→0 limh→0232+h-13-432+h+5 limh→02h+23-4h+11=2-8-4h=-14

Q: c) Consider a function f defined on the real numbers as { 0ifais irrational. S(r) = 1/n ifr= m/n…

A: To show that the function f is continuous at all irrational numbers.

Q: x² – 4, x > 2 Ax+ B,x <2 Determine the values of A and B for which the function f(x)=- will be a)…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.