Trace the curve x3y − x − 1 = 0.

Q: Find the equation of the line tangent to the curve y=x-x^2 (x squared) at x=-4

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Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

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

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Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

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Q: Sketch the curve f(x) = x/(x-1)^2. Show complete solution

A: We have to sketch the given curve f(x) = x/(x-1)2. To sktech the given curve we will follow the…

Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: Find the points on the curve xy2 = 54 nearest the origin.

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Q: Find the equation of the tangent line to the curve y2=6x-3 perpendicular to the line x+3y=7

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Q: find the equation of the line tangent to the curve at the given point x2y2=4y ;(2,1)

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Q: What is the equation of the line tangent to the graph of y = 2x³/2 at the origin? Oy=0 Oy = 2r Oy =…

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Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

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Q: Find the equation of the tangent to the curve x² +3y² = 6y at the point (1, ½)

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Q: Find the slope of the curve x2 + y3 = 2 at each point wherey = 1

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Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

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Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: This is the equation of the line tangent to the graph of * y = x2 + 3 at x = –1

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Q: Determine the slope of the curve x2+ y2– 6x – 4y – 21 = 0 at (0, 7).

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Q: The slope of the curve when x=e is y = (In 2x)?

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Q: Determine slope of a curve y = x³3 + 1 at x = 1

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Q: Find the equation for the line tangent to the curve 2exy = x + y

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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: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: 3. Trace the curve y (x-1)(x+3)'

A: Since you have asked multiple questions in single request  so we  will be answering only first…

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 for the curve dx In (2x) + 5xy + y = 3.

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

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Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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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: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: B - Find the point on the curve y = x3 + x2- 1 where the tangent parallel to the x- axis.

A: Topic- slope of tangent and application of derivatives

Q: 2.x? Sketch the curve y= x² - 1

A: y=2x2x2-1 y=2x2x-1x+1

Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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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: Parameterize the curve: x2+25y2-4x+100y+4=0

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Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

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: Determine the slope of the curve x2 + y2 – 6x – 4y – 21 = 0 at ( 0, 7 ).

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Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

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Q: Locate the inflection points of the curve y = e²x²

A: The given curve is y=e2x2. The first derivative of y=e2x2 is, y'=ddxe2x2=2xe2 The second derivative…