14) Determine all the asymptotes to each of the 3x following curves: (a) y= x-2 1 (c) y (x-(x+3) (b) y = = x²-4

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find the asymptote(s) of the given curve. 31 2x

A: The given curve is y=x2-32x-2. Vertical Asymptote: A vertical asymptote for a function f(x) is a…

Q: 6. Find the point on the curve y = yx that is closest to the point (3, 0)

A: let P is the closest point then say (x,y) then find the distance from the point (3,0)  then minimize…

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 x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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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 an equation of the tangent line to the graph at the given point. (y - 3)² = = y = 1 4(x - 5),…

A: The given equation is; (y-3)2=4(x-5), (6,5).

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: 2x Find the equation of the line tangent to the graph of y= In(3x)+- at x=1 6

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Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

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

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Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

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Q: For the curve y = ax + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: we have to solve the problem

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: 6. Find the member of the curve whose slope at any point is √y and passes through the point (2, 1)

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

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Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: Problem 4.10 Find the slant asymptote of 2x3 – 5x2 + 3x y = x2 – x – 2 and sketch the curve.

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Q: 11. Find the length of the curve y = 2x3/2 x!/2 from x = 1 to x = 4. 2

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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

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Q: 1. Consider the curve defined by 9x2 – 16 y² +36x + 96y– 252 = 0. a) Write the equation of the curve…

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Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: Find the points where the graph of 2y-x+4x-6y+1=0 has horizontal or vertical tangents.

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Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

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Q: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

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Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

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Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

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Q: Sketch the graph of y = -3 sin(x) on the axes below. 4 3 2 -7/2 7/2 37/2 27 -1 -2 -3 -4

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Q: The horizontal asymptotes of the curve 12x y = (zª + 1)'/ are given by Y1 = and Y2 = where yı > Y2-

A: Asymptotes are the tangents where the function tends to meet at the extremities of the x and y axes

Q: I need to solve this question

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Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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Q: Find the exact length of the curve. y = In (1 - x2) ,    0≤   x ≤ 1/2

A: Given, y=ln1-x2,0≤x≤12 We know the ars length formula is, L=1+dydx2dx Now we find the derivative by…

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

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