The function is on the interval くx< (segment 1), on the interval くく |(segment 2), and

Q: Show that there is a number between -2 and -1 whose double is exactly 1 less than its cube, and use…

A: Let, f(x) = x3-2x -1. Now, the required number must be root of the equation f(x) because x3-1 = 2x…

Q: Name three functions that are continuous at every realnumber

A: The name of three functions that are continuous at every real number:

Q: fx +3, x * -2 3) f(x) = ; -4, х--2 x =

A: We have to find

Q: How many bijective functions have [10] as both the domain and codomain?

A: Consider the provided question, We need to find How many bijective functions have [10] as both the…

Q: Construct three different graphs which lie on interval (-8,8). From three intervals, prove that they…

A: In the given question we have to construct three different graphs on the Interval (-8,8) from three…

Q: Sketch the graph of a function that is continuous exceptfor the stated discontinuity. Discontinuous,…

A: Given that the function is continuous from the right, at 2. But discontinuous at x=2

Q: The summation of a constant is equal to the product of the cardinal of the index set and the…

A:

Q: On which two intervals is the function increasing (enter intervals in ascending order)? to

A:

Q: Sketch the graph of a function that is continuous exceptfor the stated discontinuity.…

A: Given that: Discontinuities at  -1 and 4, but continuous from the left at -1 and from the right at 4

Q: Sketch a graph of a function that is one-to-one on the intervals 1-∞, -24 and 3-2, ∞2 but is not…

A:

Q: 91. How many x-intercepts can a function defined on an interval have if it is increasing on that…

A: An increasing function is a function which gives a greater value of the function for a greater value…

Q: How many functions map {1, 2, 3, 4, 5, 6, 7, 8} onto {1, 2, 3, 4, 5} (i.e., how many surjections are…

A:

Q: Construct three different graphs which lie on the interval (-8,8). Choose three different…

A: Let us consider the functionThe graphs of functions, f(x)=x25, g(x)=x310 and y=x+1 lies on the…

Q: Explain the two-path test for nonexistence of limits.

A:

Q: Compute limit as x goes to infinity of (square root(2x^2+3x-1))/(7x+1)

A: =limx→∞2x2+3x-17x+1multiply and divide by x2=limx→∞2+3x-1x27x+1x2=2+3∞-1∞7∞+1∞=∞

Q: Describe all the x-values at a distance of 21 or less from the number 10.   Enter your answer in…

A:

Q: The range of f(x) 3 (2х — 1)(1 — 3х) + 4x2 is О 44/9, со) О -со, 35/9] О 23/5, со) О 17/3, со) О -о,…

A: Given  fx=2x-11-3x+4x2 Here we have to find the range

Q: Is the graph continuous at (-3, 1)?

A: Given:continuous at -3,1

Q: Investigate the limit

A: The limit of the function is, limx,y→0,0x2x2+3xy+y2 As x,y→0,0 we see that the given limit is of the…

Q: Determine the intervals on which the function is continuous. %3!

A: To find: The interval in which the function fx=12-x is continuous. Concept used: The domain of the…

Q: The number of cars in a parking lot is: Discrete, Continuous, or neither Discrete nor Continuous?

A: Introduction: A variable, the values of which can be counted, is called a discrete variable. A…

Q: Use Intermediate Value Theorem to find an interval which contains 7.

A:

Q: Evaluate the limit 6x3 6x2 – 5x |- lim 7 3x 6x3 - -

A: Evaluate the limit in the following way:-

Q: How many subsets are there of {1, 2, 3, 4, 5, 6, 7} that are the range of an injective function with…

A:

Q: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: Express the interval using two different representations.

A: The real line is represented by the interval notation -∞,∞ and the corresponding inequality notation…

Q: compute the limit

A: The equation is solved using the direct method.

Q: How many surjectiive functions have domain [10] and codomain [2]?

A:

Q: Evaluate the limit 11x3 3x2 – 11x - lim 10 – 4x – 3x³ - -

A:

Q: List the intervals on which f is decreasing

A: From the given graph, it is observed that the graph of the function f increasing in the intervals…

Q: Sketch a graph of the function f that is continuous on (-∞,00) and has the following properties.…

A:

Q: What are infinite limits and how are they useful?

A: What are infinite limits and how are they useful?

Q: Find the limit by rewriting the fraction first. ху - Зу - 7x+21 lim x-3 (х.у) --(3,6) X+3 ху - Зу -…

A: Factories the numerator and cancel out common term than put the limit.

Q: @ =, compute fCl @Given the function fa)= ((+ 2x]= Round to earest tenth. et

A:

Q: Find of 3-(-1)" the Set of sequential limits

A: Given;  3-(-1)n.

Q: The principle of Analytic continuation:

A:

Q: Determine the (largest possible) intervals on which the function ƒ1x2= 2x2 - x4 (as shown) is…

A: according to given graph, given function is one-to-one in x∈-∞,∞

Q: Graph the sequence of continuous function that are  conversing on a discontinuous function

A:

Q: Find interval where f is decreasing

A: From the graph from t = 0 to t = 2   ;          f = 2 from t = 2  to t = 4   ;          f is…

Q: Find the averuge valuc of the function fcx)-4x4 on the interval [2,6],

A: Given : fx = 4x4

Q: Compute limit as x goes to infinity of (4x^3 +6x-2)/(3x^3 -2x^2+x+1)

A:

Q: How many injective functions have domain [3], codomain [101], and are not surjective?

A: Find the number of injective functions from the domain 3 to the co-domain 101 which is not…

Q: The function fin) = 8n-2 is big-O(n). True False

A: Consider the given function.

Q: Suppose fx) -2x2-3x. To compute f'(x), which Limit should be evaluated?

A:

Q: Determine whether the function shown is continuous over the interval (-5, 5).

A: We will determine whether the function is continuous over the interval (-5, 5) as following.

Q: True or False The cube function is odd and is increasing on the interval (-∞,∞)

A: Explanation:' The cube function is f(x)=x3 An odd function is the function that satisfy this…

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc A…

Q: What would a graph that is continuous on the intervals (0,2] and (2,3) but not on the interval (0,3)…

A: To discuss the nature of the graph of a function which is discontinuous precisely at the point x=2

Q: When Can Pointwise Converqance preserve boundedness?

A: To prove -  When can point wise convergence preserve boundedness.

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.