math 151 calc

please solve using python and show all steps

Directions: Use Python to solve each problem. (Template link) 1. Given f(x)=x23x1 : (a) Use the for command (list comprehiension) to evaluate the function at x=0.1,0.01, 0.001,0.0001, then at x=0.1,0.01,0.001,0.0001 to numerically estimate limx0f(x) (b) Plot f on the interval [1,1] to graphically verify your estimate in part (a). (c) Compute limx0f(x) exactly, then get a decimal approximation of this limit to compare with your estimate in part (a). 2. The Folium of Descartes is given by x=1+t33at,y=1+t33at2 (a) Show that for a=2, the curve produced also satisfies the equation x3+y3=6xy. (b) Compute the limits of x and y as t approaches 1 : i. from the left ii. from the right (c) To avoid the issue in part (b), graph the curve twice in the same command, once for 5