Exercise 1.6.101: Let x' = (x - 1)(x - 2)x². a) Sketch the phase diagram and find critical b) Classify the critical points. c) If x(0) = 0.5, then find lim x(t).

A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t=0, water containing 2 lb of salt per gallon enters the tank at a rate of 8 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t, show that the limiting concentration that is, lim c(t)-is 2 lb/gal. 00+1 Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes. Flowin = 16 Write an equation for the rate of salt (in lb/min) that flows out of the tank, where t is the time in minutes. Flow out =

3.1(2) Determines the slope of the tangent to the curve (shown in the image) at point P(4, -4). A) Using the block 2 approach (using the tables below). B) Using the approach of block 3 (limit).

1 12. lim x→1+ Vx + 2