MAC 2312 Midterm: MAC2312 F97 Test 3

1. Find the following limits: (Use L'Hopital's Rule if applicable.) es points each) 6x2 +3x-7 9x2-5x +6 b. lim1-3x c. lim 2-3x+I c. lim 2x-10 2x +10 2x-10 f. lim+25 e. lim dyê·¸ dx ax ( 5-5) 50 h. lim+4-3 i. lim g. lim lim C-53) dy ex-1 ax unce Fined X-5)(x +4 xfut3

5 limex-22 [6] 15.linn (h), 回 In χ x→2 6. lim 16. lim. (-xIn.x) 7. lim 17. lim xsin sin (2x 8. lim sin(3x) 9. lim arcsin x 10. lim 3x2-2x+13 18. lim x* 19, lim (1+x)% 20. lim- 2-4 x-2 11. lim +2r+1 21. lim x-1 22. lim 5x ば+1 In x 13. linn 23. lim x→ 0 14 lim (cosx )cos 24. lim COs r-1

3. (a) (8 points) Given n numbers zi,… , an ise the second aerivative test to find the value of minimizing the sum of the squares: f(z) = (x-x1)2 + (z-x2)2 + . . . (x-xn)2 (b) (9 points) Find the global extrema of the function f(t) t (1-t), on (0, 1], where a and p are positive constants.