(b). If f: N → R is defined by f(n) = n +1 and g:R → R is defined by g(x) = Vx. Then find, if possible, the domain for gof and fog.

Q: Find c such that the function 10 г c - || 26 х > с is continuous everywhere. c =

A:

Q: If F is an antiderivative of f on an interval I, then G is anantiderivative of f on the interval I…

A: To prove: G(x) = F(x) + C Given that F is an antiderivative of f on an interval I, that is F'=f then…

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A:

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A: The odd functions are functions that return their negative inverse when x is replaced with –x. This…

Q: Find c such that the function f(エ) 8x- 20 I > C is continuous everywhere.

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

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A:

Q: Show that the function f(x) = e1/2[(x-p)/a}° has inflection points at x = u ±o.

A: Givenf(x)=e-12(x-μσ)2 To show x=μ±σ is a point of inflection of f(x).

Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

A:

Q: In the following cases, show that the p.d.f. of Y is not a member of complete family. 1. Y: N (0,…

A: A test statistic is said to belong to the family of completeness only when it follows the conditions…

Q: Given for C[-1,1] the inner-product function (f,g)= | f(x)g(x)dx , find |F|| if f(x) =1-3x.

A: The solution to the given question is explained below.

Q: Easy Calculus question, I will rate and like! Thank you for your work!

A: We have to find

Q: f(ix, λγ) - λκ. f(x, y)

A: Given: fλx,λy=λkfx,y

Q: The antiderivative of fx), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the property…

A:

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: A continuous r.v. F(x1= === 2 × -IN 15 X has CDF X Co OBX C1 18X 16 17 **** 18

A: Given: Fx=0            x<012x        0≤x<1k            x≥1

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: For what value of b is

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Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x- 3x,…

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Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x>c To find the value of c such that the…

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Consider the following. f(x) = x 4 1 4 1 3 - x2 %D - Find the critical numbers. (Enter your answers…

A:

Q: (d) If f(x) is irreducible over Q then f(x+ a) : a e Z is irreducible over Q.

A: Use the property of reducible to start the proof.  According to the property of contrapositive, "if…

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x<0   So,…

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

A:

Q: attached

A: Linearization of f(x) at x=a is given by

Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

A:

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

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Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

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Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

A:

Q: 9) The Wronskian of the functions f(x) = -5, g(æ) = 7x² y h(x) = e3 is given by a) W(f(x), g(x),…

A: The details calculation is given below

Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x³ - 3x,…

A:

Q: Use the comparison theorem with f(x) = = 1 √x r∞ 1 •√₂ √I-1 to show that is divergent.

A: Solution is given below:

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

A:

Q: The absolute maximum of y =-x + 2x +3 on the interval [0, 3] occurs at Select one: O a. None of…

A: Simply take the derivative and equate to zero than solve for x.

Q: 1. Suppose that f(z) is analytic for lz <1 and sa Show that there is a constant c < 1 such that…

A: To prove the estimate for }f(z)| over the disc or radius r, center 0

Q: Q3: a) Let f : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its -…

A: the function is invertible if its one -one and onto. The function is one - one if f(x1)=f(x2)…

Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c.

A: We know, if f"(c) is negative then f(x) have local maximum at x=c and if f"(c) is positive then f(x)…

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: (1- a? f(x) = 1– x² if x E Q, if r ¢ Q. %3D p at which f is continuous. Prove your conclusion.

A:

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: If x = c is in the domain of f such that f'(c) = 0 and f"(c) > 0, then f has a local maximum at x=…

A: The given problem is solved below in detail.

Q: Given for C[-1,1] the inner-product function (f,g)= [ f(x)g(x)dx, find ||f|| if f(x) =1-3x.

A:

Q: what is the limit of f(t) as t approaches 3. F(t)= ((1/t)-1/3)/t-3?

A:

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2

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.