Hi, can you solve questions 1 to 4 ?please. Thank you
Implicit Differentiation of the Eight Curve The graph of the eight curve, x.-a, (xa-ya ), a·o-i shown below. 1. Solve the equation for y and use the results to graph the curve using your graphing calculator, letting a 0.5, 1, 2, 3, 4, and 5. [You need NOT draw by hand the results.] Describe the results as a changes. 2. Use WinPlot to sketch the curve as it is implicitly defined. Print the results for four different values of a. Indicate scale on the axes and display the equation with each curve. 3. Find the derivative of the explicit versions of the equation. 4. Show by implicit differentiation that xâ-' (H. y*), a O results in dy-as-e the same as the result from part 3. Show that this is dx 2x3 can be simplified further so that 4.- aty 5. Show that dx g dy-a-2' , determine the points on the curve where 6, Usin there are horizontal tangent lines and vertical tangent lines. 7. Use the results from part 5 to determine the domain and range of the eight curve in terms of a. 8. Show that the slope of a line tangent to the curve at the origin is always ±1. Use the implicit derivative for this activity.
