Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive constant. Whatdo the members of this family of curves have in common?How do they differ from each other?

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

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Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

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

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

A: Given: x=3+2t y=-12-6t            - ∞ &lt; t &lt; ∞ 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: Find the exact length of the curve. y 1x²-1-In(x), = 4 2 1 ≤ x ≤ 8

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Q: Use the guidelines of this section to sketch the curve   y =x / ( x3  -1 )

A: Given: To sketch the given curve using the guidelines.

Q: Identify and sketch the curve for x2-y2-6x = 0

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Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find the exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

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Q: Find the exact length of the curve. Ex372, 0sxs 4 y =

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Q: Find the exact length of the curve. y = 5 + 8x3/2, osxs1

A: Given: y=5+8x32,   0≤x≤1

Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

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Q: Find the exact length of the curve. 1.2 y = 1x²-1⁄In(x), 2 4 1 ≤x≤ 8

A: This question can be solved using the concept of length of curve using derivatives.

Q: Find the point on the curve 4x

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Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY Y^2 =x^2+5x−4/x−5

A: We are given the curve: y2=x2+5x-4x-5 Sketching the curve , we have :

Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: Find the exact length of the curve. 2. y = 3 x3/2 Osxs1

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Q: Find the exact length of the curve. y = (1 + x2)3/2, 0 < x < 2

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Q: Find the length of the following curve. y = 3x 2) fromx = 0 to x= 8

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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. х — 6 y = x2

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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: Find the exact length of the curve. y = 2/3x3⁄2,    0 ≤ x ≤ 1

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Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Find the exact length of the curve. + 4х 1 < x < 3 y

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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 exact length of the curve. x3 y = 1 + 4x 1< x < 3 3.

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

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Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

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

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Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: Find the exact length of the curve. 1sxs2

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Q: Find the exact length of the curve. = 3/²/₁ y 1 4x 1 ≤x≤2

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Q: Find the exact length of the curve. y = 1. 1sxs 2 + - 3 4x

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Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the exact length of the curve. 1 y = 1 < x < 2 4x

A: The given curve,   y=x33+14x, 1≤x≤2

Q: Identify and sketch the curve for: x2-y2-6x=0

A: Combine the like terms of x and y in the given equation, and then add 9 on both sides of the…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.