Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the point -5 1 y = 7 2x2 1 y = 1 3 2x2 y 3 y = x4 53

Q: Find the length of the curve y = x³/2 from (1, 1) to (2, 2/2).

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Q: Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at…

A: To Determine: Value of a, b, c and d so that curve y = a x3 + b x2 + cx + d

Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: Find the curve y = f(x) in the xy-plane that has the given properties. f(x) has a slope at each…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given

Q: Find the points on the curve 9y = x where normal to the curve makes equal intercepts with the axes.

A: Since, the equation of curve is given by 9y2=x3-(i)⇒y2=x39⇒y=±x33Differentitaing equation-(i) both…

Q: Find the length of the curve y =x/2 from x = 0 to x = 3.

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Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Q2: Find the points on the curve y 2x3 -3x2 -12x + 20 where the tangent is a. perpendicular to the…

A: Curve y = 2x3-3x2-12x+20 To find the points on the curve y where tangent is   Perpendicular to the…

Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y>0. The graph of this curve in the interval…

Q: dy 20 yx %3D

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

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Q: Find the equation of the curve, if at any point on the curve y "= 1- vĩ and it has a tange line at…

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Q: Determine the constant c such that the straight line joining the points (0,3) and (5.-2) is tangent…

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Q: Differentiate implicitly to find the slope of the curve at the given point. y³ + yx2 + x² - 3y2 = 0;…

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Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that…

Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: Find the length of the curve y = x/2 from x =| 0 to x = 3.

A: We have to find out the length of curve.

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

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

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

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Q: Find the are length of the curve x = (y² + 2)/2 from y-0 to y=1

A: First, calculate dxdy for the equation, x=13(y2+2)32  . Then, use the formula, L=∫ab1+dxdy2 dy to…

Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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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: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Find the slope of the curve at the given point. 2y5+9x9=7y+4x at (1,1)

A: The given curve is,

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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Q: Find the length of the curve y=7x-13 between y=-6 and y=15.

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Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

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Q: Find the length of the curve. y = In(secx), 0Sx</4

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Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

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Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: find the slope of the curve at the point indicated y = x - 1/x + 1, x = 0

A: Given, y=x-1x+1 and the point x = 0

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

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

A:

Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…