40. Cissoid: (4 – x)y? = x³ y (2, 2) 1 3 -1+ -2+ 2.

Q: the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your answer…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(6,0,6) on the…

A: Use tangent plane equation

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A: To find the horizontal and vertical tangents to the given curve.

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Q: Determine the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the…

A: Solutionsa)let y=mx+c —(1)Thereare two parameters of equation m & cand x intercept=-cmNow given…

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Q: 6. The ellipsoid + y2 + z2 = 4 and the plane y = 1 intersect to form an ellipse. Find slope of the…

A: Given:

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Q: Find the family of curves for which the slope of the tangent line at (x, y) is (1+x)/(1-y).

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Q: 3Keth curve ,Orienlation, regtangular equation. X = t-1 1-7

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A: Given: Slope of tangent line is given as:

Q: curves about the x-axis. y = x, y = 0, x = 2, x = 3 O 1 O 13 O 19

A: We will find the volume of the region.

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A: If , then the independent variable x is called the input of the function and the dependent variable…

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Q: Determine the equation for tangent and normal at the point with x -coordinate 1 on the curve y = 2…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the…

A: solution

Q: Consider the curve parameterized by x 3t2 3 and y 2t°. Find equations for all tangent lines to this…

A: Here we have to find the equation of tangent line.

Q: 24. At what point(s) on the curve (y - 2)² = x is the tangent line vertical? The tangent line is…

A: The given curve,   y-22=x

Q: (a) Given that the transition curve of the highway is modelled after the curve y=4sin x-sin 2 x.…

A: Guven curve  y= 4sinx-sin2x. We have to find its curvature at x=pi/2.

Q: Application of Ahe derivative 2) If the curve with eanation y= 2c? +ax +S has a Stationary point…

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Q: Find the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the…

A: Ans (a). Given that, There is a straight lines with slope half the value of the x-intercept. let…

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A: I have written the important facts in the solution part

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Q: 2/3 10. Find the equation of the tangent and normal to the curve y = x+ x3 at (0,0).

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Q: Find an equation of the tangent plane to the surface at the given point. (2,0,0) g(x, y) = arctan…

A: Answer and explanation is given below...

Q: With a curve 56 3 17 x² + y = 6, y = x, y = -2 and x = -2. . Determine its area.

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A: We have to find value of t for horizontal tangent line and vertical tangent line .Now x and y…

Q: Consider the family of curves y I 1+ GI

A: We have y=x1+c1x Differentiate with respect to x: dydx=ddxx1+c1x⇒dydx=1+c1xdxdx-xd1+c1xdx1+c1x2…

Q: equation of the tangent plane to a surface z = f(x, y) = ln ( /4x² + 9y² + 2x at the point P(-2,1).

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

Q: 3) Find a point on the curve y = 1+ 2e" – 3x where the tangent line is parallel to the line 3x – y =…

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Q: 4- x Find the equation of the tangent line tof-l at the point P (G, 1) for f(x) = x+1 Provide your…

A: Topic:- application of derivatives

Q: Find the slope of the curve x^3=(y-x^2)^2 at (1,2). If q-p=Inq+Inp, find dq/dp.

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the given point. Verify your…

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Q: Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility…

A: Given that: x=6-t and y=t2

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Q: Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to…

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Q: A telephone line hangs betweenn two poles at 12 m apart. In the shape of the catenary y = 50 cosh…

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Q: ential equation of the family of curves y B are arbitrary constants

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Q: Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to…

A: In order to find the vertical tangent first differentiate x with respect to t  and to find the…

Q: 6. Determine the point of inflection on the curve defined by y=x³ + 5. Show that the tangent line at…

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

Q: The plane y = 1 intersects the surface z = x4 + 6xy - y4 in a certain curve . Find the slope of the…

A: Given :Plane y=1 intersects the surface…

Q: a. Find a curve y = f(x) with the following properties: i) = 6x dx² ii) Its graph passes through the…

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Q: FINDinG THE cauaTIon OF THe cUrve CURUC WHOSE y": 12 x- 24 WITH A HORI ZONTAL tAnGent AT THE POint…

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Q: Find the critical values of y = x - 2x and determine their nature. Sketch the curve.

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Q: Find the points on the curve where the tangent is horizontal or vertical. x = t3 − 3t,    y = t2 −…

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Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark…

A: Solution is done in step 2