Write the equation of the curve that is the intersection of the surface and the plane. Find the slope of the tangent line to this curve at the point (2, 1, f (2, 1)).

Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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Q: Find the equation of the tangent plane to the surface at the specified point.

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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: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Write the equation of the line tangent to the curve xey = 2y + 3  at (3, 0).

A: We have to write the equation of line tangent to the curve xey=2y+3 at the point 3,0 We know that…

Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

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Q: Find the equation of the tangent plane to the surface 4 =1 at the point 9. 16 (1,-3,2)

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Q: find the equation of the tangent plane of this surface

A: In this question, we check the surface is simple and then we find the equation of tangent plane at…

Q: Find an equation of the tangent plane to the given surface at the specified point. 2. (-16, 4, -1)

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Q: Find the equation of one of the tangent lines to the circle x^2 + y^2 = 5^2 that passes through the…

A: Here, to find the equation of the tangent line to the circle  x2+y2=52⇒x2+y2=25...(1) that passes…

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

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Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

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

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Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

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Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

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Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y? - 32? . = 82, (-7,…

A: Given equation  x2+y2−3z2=82,     (-7,-6,1)

Q: Find the equation for the line tangent to the curve 2exy = x + y

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Q: Find an equation of the tangent plane to the surface at the given point. x²+²-72²-38, (-3, -6, 1)

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Q: Write a parameterization for the curve in the xy-plane that is a vertical line through the point…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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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: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

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Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

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

A: Now when x = 3, we get Therefore the point (3, -4) is on the given curve. a). Slope of the tangent…

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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Q: Find the equation of the tangent plane to the surface 4 = 1 16 at the point 9. (1,-3,2)

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Q: Write the equation of the line tangent to the curve xe = 6y + 7 at (7, 0). %3D

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Q: Sketch the curve and find the axis. y = Sinx; [0,] 2

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

Q: Find the coordinates of a point on the parabola y=−x² where the slope of the tangent is 5. x+3x+4

A: The given parabola is y=-x2+3x+4 We need to find the coordinates of the point on this parabola where…

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: Find the angle of intersection between the curves y = x- +1 and y = x+x-

A: y = x2 + 1,y = x+ x-1Points of Intersection;x2 + 1 = x+1xx(x2+1) =(x2+1)x = 1y = 2point of…

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 tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

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Q: Find the slope of the tangent line to the curve 2x + lay 4y 20 at the point (2,- 2).

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find an equation of the tangent plane to the surface at the given point. + 3x – z2 = 56, (5, -3, 2)

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Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

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