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13 Nov 2019
CALCULUS PROJECT: Implicit Differentiation of the Eight Curve The graph ofthe eight curve, x· ,a), o-isshown below. 1. Solve the equation for y and use the results to graph the curve using your pra cakulator, letting a- 05.1,2.3,4, and 5. [You need NOT draw by hand the rosuts] Desenibe the results as a changes 2. Use WiaPlot to sketch the curve as it is implicitly defined. Print the results for four different vallues of a Indicate scalk on the ases and display the equation with cach curve. 3. Find the derivative of the explicit versions of the equation 4. Show by implicit differentiation that r'-a%, y, a-0 the same as the result from part 3. 5. Show that空 2x, can be simplified further so that a1-2 Show tha this is 2. 6 Using-2 there are horizontal tanget lines and vertical tangent lines 7. Use the results from part 5 to determine the domain and range of the determine the points on the curve where eight curve in tems ofa 8 Show that the slope of a line tangent to the curve at the origin is always ì¹. Use the implicit derivative for this activity.
CALCULUS PROJECT: Implicit Differentiation of the Eight Curve The graph ofthe eight curve, x· ,a), o-isshown below. 1. Solve the equation for y and use the results to graph the curve using your pra cakulator, letting a- 05.1,2.3,4, and 5. [You need NOT draw by hand the rosuts] Desenibe the results as a changes 2. Use WiaPlot to sketch the curve as it is implicitly defined. Print the results for four different vallues of a Indicate scalk on the ases and display the equation with cach curve. 3. Find the derivative of the explicit versions of the equation 4. Show by implicit differentiation that r'-a%, y, a-0 the same as the result from part 3. 5. Show that空 2x, can be simplified further so that a1-2 Show tha this is 2. 6 Using-2 there are horizontal tanget lines and vertical tangent lines 7. Use the results from part 5 to determine the domain and range of the determine the points on the curve where eight curve in tems ofa 8 Show that the slope of a line tangent to the curve at the origin is always ì¹. Use the implicit derivative for this activity.