Determine the parameter equation of the following curve x2 + y2= 5

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: Use the guidelines of this section to sketch the curve.   y = x/ x-1

A: To find the x-intercept we plug y=0 So x-intercept is 0 To find the x-intercept we plug x=0 So…

Q: Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine…

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Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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

A: Here is the solution of the given problem.

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Find the x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

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Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

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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: Find the slopes and equations of the lines tangent to y = f(x) at the given point.

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

A: v

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: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

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

Q: Find the equation of the line segment tangent to the curve y−2x^2−1=0 which is parallel to the line…

A: Given curve is y-2x2-1 = 0

Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

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

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Q: dy 20 yx %3D

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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: 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: A curve is defined by the equation xy - 6+x?y = 0. (a) Verify that the curve passes through the…

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Q: Use the guidelines of this section to sketch the curve.   y= 3√(x3 + 1)

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

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

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Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

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: dy 20 yau

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Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: Consider the curve described by the equation 2y2-x2 = 4y. Then verify that the point (4,-2) lies on…

A: Given curve is -  2y2 - x2 = 4y  To check whether (4,-2) lies on the curve , substitute the point in…

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: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

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

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Q: Find the inflection points of each of the given curve.  y = 5x – x5

A: Given :y=5x-x5

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

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Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: The given curve is rotated y = 3 - x2,

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Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

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

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Q: Find the equations of both of the tangent lines to the ellipse x² + 4y² = 36 that pass through the…

A: Find the slope of curve. Find the derivative of the following function.

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…

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

Q: 1 Find the stationary points and state the nature of the curve y=xe.

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