Q1) Find the distance between the oblique asymptote of the function f(x) E***-4 and the x²-2 center of the circle y+x+4x+2y31.

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: To find the critical points we solve dy/dx=0

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: Find the oblique asymptote of 2z2-9z+15 f (x)= I-5 Section 3.4 O y = 2x + 1 y = 2x-19 O y = 2x- 9 O…

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Q: Find the horizontal and vertical asymptotes of the curve. x2 + 1 y = 9x2 - 26x – 3 (smaller x-value)…

A: From the given problem: y=x2+19x2-26x-3 To calculate vertical asymptote, equate denominator to zero…

Q: Solve and find limt→∞ y(t) of y′′ + 5y′ + 7y= 0

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Find the minimum distance from the point (3, 0) to the circle x2 + y2 = 4.

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Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: 1. Sketch the graph of y = sinx,0 ≤ x ≤ 360°, and complete the table below Maximum: Minimum:…

A: This question is based on graph of y=sinx

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: The horizontal asymptotes of the curve 3x y = (x4 + 1)'/4 are given by %3D Y1 = and Y2 = where y1 >…

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Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: Find the asymptoles of the funchon given Hx)= x²- 5x+6 below X-2

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Q: Find global maximum and global minimum of æ3 – 9x? – 48x + 52 on the interval [-5, 12]

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Q: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

Q: G&)= In (5x t10) + 1, 1 State and domain, vertical asymptote end behavior. As approches vertical, Gx…

A: Let G(x)=ln(5x+10)+1.1 The domain of the function is the set all x-values on which the function is…

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: . Consider the accompanying graphs of y = 2r + 3 and y = In x. Determine the a. minimum vertical…

A: Given, y=2x+3 and y=lnx. And, the graph is shown below: a. Let Ax,y=x1,2x1+3 and Bx,y=x1,lnx1 be…

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find the asymptotes of the curve y3+x2y+2xy2-y+1=0.

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Q: A baseball is launched into the outfield on a parabolictrajectory given by y = 0.01x(200 - x). Find…

A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: 2. Sketch the parabola: f(x) = x² - 2x - 3. Graph -6 Domain Range (Label x and y intercepts and…

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Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Givenf(u)=8u-316u2+6

Q: Wrat is the equation in standard form of ahyperbola whose asymptotes are y=- うオー and y= -x- and a…

A: Given: y=32x-92         asymptote 1 to hyperbola                                         1y=-32x -32…

Q: 4. that has the asymptotes x 7 and y = 6. Write an equation for the translation of y = 4 Oy=ー+7 -6 4…

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Q: Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which…

A: Label the points on the given graph as shown below.

Q: Find the horizontal and vertical asymptotes of the curve. 2ex y = ex – 6

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Q: Find the horizontal and vertical asymptotes of the curve. 6x²+x- - 9 у x² + x - 56 X = (smaller…

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Q: The graph of x + z² = 1 is an ordinary right circular cylinder. Indicate axis of the cylinder lies…

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Q: Determine equation in factored form for the function, f(x), shown on the graph. y Intercept (0,6)…

A: By looking at the graph it can be said that the function is of order 3. Here, the x-intercept is…

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: Suppose that/ (3r-x²) dr=Ax'+Bx'+C, for constants A, B, C. What is the value of C if the curve =…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: 1. Find the absolute minimum and maximum values taken by the func- tion f(x, y) = x² + y² – x – y +1…

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Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Q: Find all asymptotes of the curve x2 + 3xy + 2y2 + 3x – 2y + 1 = 0 ?

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Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12