(c) Sketch some typical members of the family of curves y = ax? + b.

Q: 2. 3x + 4y +c = 0

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Q: Use the guidelines of this section to sketch the curve.   y = x/ x-1

A: To find the x-intercept we plug y=0 So x-intercept is 0 To find the x-intercept we plug x=0 So…

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

A:

Q: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x- 5), (9, 7) %3D…

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Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: Sketch the following family of curves. 1. 3x + cy – 12 = 0 %3D

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Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Locate the points of inflection of the curve y = (x^2)(e^x) * -2± /3

A: Solve the following

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

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Q: Determine the nature of the turning points for the curve y = x^5 − 5x^4 + 5x^3 − 1.

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Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: 2. Find the slope of parabola y = ²+3 at any point on the curve.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Consider the curve given by the equation 0 = y3 +xy +2ax + 1+x4  y'(0) = ?

A: Answer and explanation is given below

Q: The a coordinate of the point of intersection between the two curves y = ellz and y= 1 is x =

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Q: x3 Y2 = x2-4x+4

A: To determine the properties of curve, we will need to have function, its first order derivative and…

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: Find the coordinate of the extrema of the curve y = x² – 4x + 1.

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

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line.…

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

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: 9. Find the point of intersection of the two curves, * y = 2r-1 y = x-2r O(-) none of these

A: To find out the point of intersection of curves.

Q: Use the guidelines of this section to sketch the curve   y = x (x- 4 )3

A: Consider the given function: y=xx-43 Now make a table for function value at different points:

Q: What is the equation of a family of curves orthogonal to 2x2 + y2 = c?

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Q: Use the guidelines of this section to sketch the curve.   y= 3√(x3 + 1)

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Q: (x – 2)2 + y² = c² %3D

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Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

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Q: After Identifying and sketching the curve for x2+25y2-4x+100y + 4 = 0, partimize the curve

A: Given: x2+25y2-4x+100y+4=0 To Find: i. Identify and sketch the curve.ii. Parametrize the curve.

Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Use the guidelines of this section to sketch the curve   y = x e -1/x

A: The given function is y=xe-1x. Sketch the graph of the above function as shown below.

Q: Sketch the curve: y² = Xー4

A: A function is an equation that connects the variables x and y. In the xy plane, a function…

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

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Q: The curve is given by 2 + 1), 0<x<3. 3

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Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

A:

Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: At what points does the curve defined by x2 + 16y² – 16 = 0 have the following? (a) horizontal…

A: Tangents are line that are drawn to a point on function curve such that, it just touch the function…

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: a) y = x? e-X

A: We have to discuss properties of the graph