Lecturel'lireel't'actiuuL;xa1m|445 Practice Exam Find the critical numbers of the following lnction on the given intervals. Identify the absolute maximum and absolute minimum values (if possible). 1. f(9)=sint9, %3635?\" 2. f[x]=.r21 1.r$2 Find the critical numbers and the open intervals on which the function is increasing or decreasing. 3- fv>=x f4x2 4. g(x)=x4 4.73.4.2 Find the critical numbers and identify the function's local extreme values. 5. f[x]=x]22:1 6. f(x) = 4x3 8x2 +32 Find the points ofinection and where the graph is concave up and down. 7. f(x) = %x4 3x2 +4x+l 3. f(x) = 4x3 8x2 + 32 Evaluate the following limits using l'Hpital's Rule 9- llm x3 l 11. lim Slnx;2 13- \"m 2X5 fX'll I>1 4x3 .r3 'YFO 7x IH'O 5x6+r 2r a - e l+2x x 10. lim {51 12' Jinn 2 14. lim (11] I\" x ] ' x xwo x 15. Whenever a person coughs, the radius of the main air passages to the lungs decreases. We wish to determine at what radius the velocity of the expelled air will be maximum. Let v denote the function which gives the velocity of air through a particular air passage at a radius r of that passage. Under usual conditions, it has been found that the following relationship prevails: v(r) = cr2[r0 r) where c' is a positive constant and r0 is the radius of the air passage at atmosphere pressure. 16. A rectangular page is to contain 24 squares inches ofprint. The margins at the top and bottom 1 2 the dimensions of the page be so that the least amount of paper used. ofthe page are 1 inches, and the margins on the left and right are to be 1 inch. What should