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Q: Suppose ƒ is an even function and Evaluate

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Q: Find the value of 0x/0z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x ...

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Q: What is a conditionally convergent series?

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Q: Give the domain and the range of the quadratic function whose graph is: Minimum = 18 at x = -6

A: Given, The minimum of the graph of quadratic function is 18 at x = -6  

Q: Find the derivative of the function

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Q: Approximate the area under the graph of F(x) = 0.7x° + 7x - 0.7x-7 over the interval [-7,-2] using 5...

A: Given, The area under the graph of f(x) using the left Riemann sum is given by where,

Q: Using a graphing utility Use a graphing utility to graph the following equation. In the case, give t...

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Q: F(x) = f ∘ g ∘ h. Identify functions for f, g, and h.            F(x) = 1/4x6

A: It is given that  where Now, consider the functions as        

Q: Integrals Evaluate each integral.

A: Let the given integral is,

Q: How does the periodicity of /(0) = sin0 and /(0) = cos 0 follow from the unit circle definition?

A: Periodicity means that after the same range, same set of values gives the same result. y=sin 0 repre...

Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the para...

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the pa...

Q: Graph g(x) = x sin (1/x) to estimate limx→0 g(x), zooming in on the origin as necessary. b. Confirm ...

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Q: A landlord needs to update a rental house due to it's age, so it can be habitable again. If he has t...

A: Given: Monthly payment PMT = $1,400.00 Rate of interest = r = 3% = 0.03 Number of years = t = 2 year...

Q: Use the Table of Integrals  toevaluate the integral

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Q: Find fy. f(x.y) = x"6 – 5x²y23 + 4y 7 5x y f(x,y)% 3Dx

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Q: Identify the inflection points and local maxima and minima of thefunctions graphed. Identify the int...

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Q: please solve and graph

A: Given, the integral                      

Q: Fill in the blank/s : tan(θ - φ) = ___________

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Q: write standard equation for the graph

A: Given a graph of hyperbola.

Q: Big (Lack of) Men on Campus In 2007, 135 women received bachelor’s degrees for every 100 men. Accord...

A: Given Data The mathematical model of the percentage of bachelor’s degree awarded to men is M=-0.28n+...

Q: Solve the differential equation.  dy/dx=(x-2)/sqrt(x^2-4x+5)

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Q: How are vectors added and subtracted geometrically? Algebraically?

A: Vector addition or subtraction can be done by Geometrically by two methods. Let there are two vector...

Q: Given that {an} is a decreasing sequence and all its item lie between thenumbers 5 and 8. Explain wh...

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Q: Find the interval of convergence of the power series n3 n=1

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Q: Consider the helix represented by the vector-valued function r(t) = ⟨2 cos t, 2 sin t, t⟩.          ...

A: We have given that; A helix represented by the vector-valued function r(t) = ⟨2 cos t, 2 sin t, t⟩

Q: 1. Why do we know that the inner quadrilateral inside the square is itself a square? 2. Calculate th...

A: (1) Each side length of a quadrilateral is the same which is c. Since the quadrilateral of the same ...

Q: A company is producing a new product. Due to the nature of the product, the time required to produce...

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Q: 2x +5 dx = ? x+4x +13 X

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Q: Let v = (8, 15). a. Find a vector in the direction of v that is three times as long as v. b. Find a ...

A: Given vector            

Q: Find the solution of the exponential equation100(1.03)2t=50,000100(1.03)2t=50,000in terms of logarit...

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Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2 ...

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Q: Determine how many terms of the following convergent series must be summed to be sure that the remai...

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Q: Prove the following identity: csc^2Atan(2A)=2cosAcos(2A)sinA

A: To prove the identity:

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given...

A: We have given the integral function; We know the trapezoidal rule;

Q: solve the initial value problem. 4y'' + 4y' + 5y = 0, y(p) = 1, y'(p) = 0

A: Given differential equation With initial condition  

Q: Evaluate the limit.

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Q: Integration by parts with u = Inx, dv = x dx

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Q: Determine a particular solution to the given differentialequation of the form yp(x) = A0e−3x. Also f...

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Q: Write tthe history of Mathematicain Maclarurian and maclaruian series importance of mathemtica serie...

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Q: Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and a...

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Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2...

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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.