Consider the curve y = 4x3. The sketch of the portion of this curve between x = - 1 and x = 8 is presented below. y 16 -1 1 8

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

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: Find the length of the given curve. 4/3 3y2/3 X = -27 - 32

A: The arc length formula is L=∫ab1+f 'y2dy. Here, 3y43-3·y2332' =-1+64y2316y13. Thus, the length of…

Q: Sketch the ff curves: a) Y = x² e* b) Y = 1+lnx c) Y = ²-4)² x-4

A: To draw the graph of asked curves you can simply make a table and find some points through the curve…

Q: Given the x²-xy +y² = 9 %3D Curve Write general expression for the Slope curve.

A: The given equation of curve is x2-xy+y2=9. Differentiate both sides of the above equation with…

Q: The curve's equation is given by x* + y4 = x² + y?

A: Here is the solution of the given problem.

Q: find the properties of the curve ans sketch fully 6. Y^2 = (x^3)/(x^2 -4x +4)

A: Consider the given function. y2=x3x2-4x+4 There is y2 Therefore the value of y can be a positive or…

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

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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: Evaluate Pw.-(x+2y))- dr, where C is the curve shown below.

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Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

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

A: Answer and explanation is given below

Q: Q2- Sketch the curve: y = (x+1)

A: The function given to us is  y=x(x+1)2

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: Find the coordinates of the stationary points for the curve  y =-x3 -4x2 + 3x +18. Determine the…

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Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

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: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x3 – 3x² + 4x – 12…

A: Given: (1)  y=x3-3x2+4x-12 (2)  y=x2-52

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

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

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

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

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: I Discuss the properties of the curve and sketch fully: a) y = x? e-x 1+2nx b) y = =

A: Get  the asymptote of equation in a: y=limx→∞x2e-x   =0 Thus, plot the graph:

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: Jse the guidelines of this section to sketch the curve. y = x2 - 4 y y 5 X 5

A: Given that: y=xx2-4

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: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

Q: Q2- Sketch the curve:

A: We have to sketcht the curve y=x(x+1)2

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

A: Given The equation is y=3x5-5x3+4.

Q: Y = 3x5 – 5x3 + 4

A: Given function is: f(x)=3x5-5x3+4 Given function is polynomial function whose domain and range are…

Q: 2.x? Sketch the curve y= x² - 1

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

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

A:

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

A: Differentiating with respect to y, we get

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 length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY 6. y2 = x²+5x-4 x-5

A: Given, the function y2=x2+5x-4x-5. We have to sketch the given curve. Also, find the properties.

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 the exact length of the curve. y ‹ = ²(1 + x²j³/2₁ 3/2, 0≤x≤ 5

A: The objective of the question is determine the length of the given curve.

Q: 9. What is the slope of the curve at the given point? 5x? + 2xy – y = -3 at (,2)

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Q: a) y = x? e-X

A: We have to discuss properties of the graph