Providing a proper explanation, trace the curves: (1) a?a = y°(2a - y), where a > 0,

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

A: Given the curves y=ax2+b is parabola  For a=1, b=0 y=x2

Q: Q/ Find the angle between two curves: 3 y = ==- x? , y = x? 2

A: The angle between the two curve is                                         tan θ =m1-m21+m1m2…

Q: Sketch the curve (2² + y*)³ = 4.x²y? 2.2

A: To sketch the graph of:(x2+y2)3=4x2y2

Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an…

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2(2? + y?)? = 25(2² – y²) at the…

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Q: a curve like y=x/1+1x^2 is called a serpentine. Find an equation of the tangent line to the curve…

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. =…

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Q: Find the slope and concavity of the curve at the given points. r = 1/u, u = -pi, 1

A: Solution:Given    r=1u, u=-π,1To find the slope and concavity of the curve.Formula:Slope of the…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(2 + y²)° at the point (- 3, - 1) 2.…

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Q: Describe the shape of the curve x = 3 cost,y = 3 sin t.

A: We have to describe the shape of the curve x=3cos(t) ,y=3sin(t)

Q: Discuss the properties of the curve and sketch fully (drawn to scale) Y = 3x5 - 5x3 + 4 Y = (2x –…

A: As per authoring guidelines, if the question number is not specified, the first question is…

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

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &  x-2y = 6y…

Q: NO. DATE L Find the equation of the line tangert to the curve 4= x? coxo+ Ex +2 - at its point of…

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Q: consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans: 3

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Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

A: For any curve y=f(x), slope of tangents and normal at any point x1, y1 can be given by mT=dydx(x1,…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 2. y = (x2 – 3)2

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Q: Find the slope of the tangent line to the ellipse (x2/36) + (y2/49) = 1 at the point (x,y). slope =…

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Q: y =(+ + +)* x = 4t + 1, 4

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Q: sketch the curve ƒ(x, y) = c together with ∇ƒ and the tangent line at the given point. Then write an…

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Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: Q3/ Find the angle between two curves: 3 x2 , y = x² y = 2

A: Please see the answer in step 2

Q: DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y x- 3x2 + 4x- 12 2. y =…

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Q: Use the guidelines of this section to sketch the curve.

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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: DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. Y = 3x5 – 5x3 + 4 2. Y =…

A: Given function is: y=3x5-5x3+4 The graph of this function is as follows:

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x – 3x? + 4x – 12…

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Q: The equation of the curve is y? = x' + 8x. Find the x-coordinates where tangent lines are vertical.

A: We are given equation of curve  Y^2 = x^3+8x We have to find points where tangent lines Are vertical…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx %3D

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Q: xy = -4 and y² = 2х

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Q: Form the diffrential equation representing the family of curves y = a sinx (x + b) where a,b are…

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Q: Discuss the properties of the curve and sketch fully (drawn to scale) Y = (2x – 1)2 (x2 - 9)

A: Given: y=(2x-1)2(x2-9)

Q: Find the rectangular coordinate equation for the curve x= cost and y=1-sin2t for 0 greater or equal…

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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: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

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Q: a. Determine the points where the curve 5x + 3y - y= 5 has a vertical tangent line. b. Does the…

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ? O A. X…

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Q: Symmetric with respect to the y-axis yA 1 1+ x?

A: Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the…

Q: (i) On the same diagram, sketch the eurves y? =-* and y x (ii) Find the exact r-coordinate of the…

A: The solution is given below in the next step:

Q: Discuss the properties of the curve and sketch fully: a) y = x2 e-x b) y = 1+lnx

A: To sketch the curve : a) y = x2e-xb) y = 1 + ln xx

Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the…

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Q: Discuss the properties of the curve (w/ solution) and sketch fully: y = x?e-*

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Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * O…

A: The curve has an equation x=y3 K=IxA K= Radius of gyrationIx=Moment of inertia/Secon moment of…

Q: At what point do the curves ri(t) = (t, 4 - t, 63 + t) and r2(s) = (9 - s, s - 5, s?) intersect? (x,…

A: Introduction: When two vector-valued functions are given, their point of intersection can be…

Q: Exercise To Try 19 Find the equation of the tangent line to the curve below at the point (1, 2). +…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Sketch the curve y = x^3 - 3x. Remember to choose a suitable scale.

A: y=x3-3x x-intercept: (y=0) x3-3x=0x(x2-3)=0x=-3,03 (-3,0) ; (0,0) ; (3,0) y-intercept: (x=0)…

Q: find equations for the lines that are tangent andnormal to the level curve ƒ(x, y) = c at the point…

A: given: ƒ(x, y) = c at the point P0 y - sin x = 1, P0(π, 1)

Q: A curve is defined by the equation 2sin(y) – xy + y2 = 0. (a) Verify that the curve passes through…

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