Trace the curve of the following equations: 1. y = (x^2 + 2x + 1) (x-4) 2. y^2 = x^2 +5x +7

Q: Graph the curve with equation ỹ° - 1)(y – 2) = x(x – 1)(x – 2) At how many points does the curve…

A: According to question, Given equation of curve, yy2-1y-2 = x x-1x-2             ........(1)

Q: EVALUATE. Find the equation of the family of curves whose slope at any point (x,y) is -4e-2xsin2x.…

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Q: Find parametric equations for the curve with the given properties. The line passing through (5, 7)…

A: Given that the line is passing through (5, 7) and (6, 8) So the direction vector of this line is:

Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through…

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Q: (1 point) Find the slope of the tangent line to the ellipse 16 1 at the point (r, y). 25 slope = Are…

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Q: (6) slope: .. y-intercept:. Equation: .

A: Given that:

Q: curve Y = √x closest to the point (5,5

A: The given curve is y=x.

Q: A curve passes through the point (0,6) and has the property that the slope of the curve at every…

A: As we know that, the slope of the tangent line to the curve at Px,ya point is given by: dydx. Given:…

Q: a. Find an equation for the line that is tangent to the curve y = x3 - x at the point (-1, 0). b.…

A: (a) Consider the provided equation of curve and point where the tangent drawn is shown below,

Q: 7. (1 point) Find equations for two lines through the origin that are tangent to the ellipse 212 –…

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Q: Jorge starts 2 feet in front of a motion detector. For the first 3 seconds, Jorge walks away from…

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Q: conicd Clasty form- k veduce the relation to

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Q: (8) slope: y-intercept.. Equation:

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Q: Y = (2x – 1)2 (x2 - 9) %3D

A: Given that, y=(2x-1)2(x2-9) The y is zero is, (2x-1)2(x2-9)=0(2x-1)2=0,…

Q: Find equations of the tangent lines to the curve y = (6 In(x)) at the points (1, 0) and at the point…

A: Solve by using equation of tangent

Q: Find the equation of the tangent line to the curve y=5x /1+x^2 at the point (4, 20/17) The equation…

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Q: A curve passes through the point (0,5) and has the property that the slope of the curve at every…

A: Slope of the curve is given by dy/dxdy/dx is twice the y coordinate. So, dy/dx=2y

Q: Circles Two circles of radius 4 are tangent to the graph of 4x at the point (1, 2). Find equations…

A: We have given that two circles of radius 4 units are tangents to the graph of y2=4x at the point 1,2…

Q: The number of bacteria, per unit of volume, existing in a culture after x hours [0, 1, 2, 3, 4,...]…

A: Given 2 mathematical models. We need to compare the given data of values and find which of them is…

Q: Line tangent to an implicitly defined curve. Find the equation of the line tangent to the graph of…

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Q: a) The curve with equation y2 =5x4 -x2 is called akampyle of Eudoxus. Find an equation of the…

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Q: Find equations of the tangent lines to the curve y=(5ln(x)) / x at the points (1,0) and (e, 5/e) at…

A: Given that the equation of the curve is        y = 5ln(x)/x   at the point (1,0) and (e,5/e) .

Q: A curve passes through the point (0, 6) and has the property that the slope of the curve at every…

A: Given that the slope of curve at every point is twice the y-coordinate at P. i.e. dydx=2y (as dydx…

Q: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

A: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

Q: (a) Equation of the circle of radius 2 centered at the origin(b) Equation of the circle of radius…

A: (a) Given Data: The expression to generate the equation of a circle with radius r and center at…

Q: 3: One way to try to determine the line of intersection of two planes in 3-space is to find two…

A: The Geometric Idea behind the method is as follows: By putting on dimension equal to zero, the…

Q: Equation of the circle whose center is the centroid of the triangle with vertices (-7,2), (4-3),…

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Q: (a) Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line. (b)…

A: a)  we need to find all the points of the graph that have a horizontal tangent line For that, let…

Q: Graph and calculate the relation of the equation x2/4+y2/16 = 1 using the points calculated in the…

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Q: A straight line from the origin passes through the point P(x, y) in the first quadrant and is…

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Q: For a certain curve, the point of contact of each tangent to it bisects the part of the tangent…

A: For a curve, the point of contact of each tangent to it bisects the part of the tangent terminating…

Q: Two circles of radius 8 are tangent to the graph y^2=4x at the point (1,2) Find equations of these…

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Q: passes through the points (-2, -9) and (4, -6)

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Q: For a certain curve, the point of contact of each tangent to it bisects the path of the tangent…

A: Let xa+yb=1 be the tangent. Let the tangent cut the axis at a,0 and 0,b. So the mid point of the…

Q: lly: y^2= x^2+5-4/x-5

A: Given: To find the properties and sketch of the curve, y2 = x2+5x-4x-5

Q: (3) slope: y-intercept:. Equation:

A: We need to find equation,slope and y intercept of the line given on graph

Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 10 -5 -2 -5 4-3 -2 -1 0 1. 5 6 -4 -5 -8 -9 -10 -11 -12 -13 8. 5. 3. 2. 7. y-axis

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Q: Oil spills from a tanker in the Gulf of Mexico and surfaces continuously at coordinates (x, y) =…

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Q: 1. Find the equation of the family of curves whose slope at any point is 6x. Find also the equation…

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Q: Consider a circle with center at the origin and with radius 3. a What is the equation of the circle…

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Q: 8) About the y-axis (0, 2) л y = 2sin (x) ;0< x≤ π X X

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Q: 2. Center: (2, -1) Focus: (2, -31) Vertex: (2, 23) (v+1)° ¸ (x-2)² [A] = 1 576 324 (y+1) _ (x-2)*.…

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Q: Calculus MAT 301 Lab #3: 1) Plot the curve x^3+y^3=6xy together with the tangent to the curve at…

A: Solution of the problem as follows

Q: Find the equations of the tangent line and normal line to the curve y = x3- 2x 1+ at the point (0,…

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Q: A cell phone tower is located at (5,-2) on a coordinate plane with units in kilometers. What is the…

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Q: Use a graphing utility to sketch the intersecting graphs of the equations and show that they are…

A: Orthogonal curves are the curves whose tangent lines are perpendicular at every point of…

Q: (5) slope: y-intercept:. Equation:

A: observe the graph

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.