Find the slope of the tangent line to the ellipse 1 at the point (x, y). 9. slope = Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.) slope is undefined at

Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

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Q: 9. Find the angles at which the curve y =x - x intersects the x-axis.

A: Given: The curve y=x3-x intersects the x-axis

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Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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

A: consider the equation of the ellipse, x24+y216=1 differentiate the equation using implicit…

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 exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

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: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

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Q: Find an equation of the tangent plane to the given surface at the specified point. = 4(x – 1)2 + 3(y…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Determine an equation for the tangent plane to the graph of z = 2 + 2 vy + - 7 at the point (1, 2,…

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Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

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Q: Find the slope of the tangent line to the ellipse = 1 at the point (z, y). 36 slope = Are there any…

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Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: e tangent line to the ellipse 25 = 1 at the point (x, y). 9. %3D s where the slope is not defined?…

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Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find the slopes of the tangent lines to the ellipse 4x +y = 40 at y=2. The smaller slope is The…

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Q: Consider the curve parameterized by x = 2t³ - 33t² + 180t and y = 2t³ + 33t² + 180t. At what points…

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Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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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: Below is a plot of a cardioid, which consists of points satisfying x² + y² = (2x² + 2y² - x)² 0.6…

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Q: Find the exact length of the curve. y = 5 + cosh (2x), 0≤x≤ 7

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Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

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Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: Determine an equation for the tangent plane to the graph of z = 2 2 +2 ay+2y2 - 4 at the point…

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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: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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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: 2) Find and sketch the circle of curvature at the point on the curve y = x² where the tangent line…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

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: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

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: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

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 tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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