MATH 1A/1B REVIEW PROBLEMS DIRECTIONS: In each problem below answer TRUE if the statement is always true and FALSE otherwise. Enter your answers on a SCANTRON form 882E or any SCANTRON form with 30 or more questions on it. Our bookstore has plenty of these. Submit your SCANTRON form on the day listed on the course calendar. 1. 2. d cos 3 x = 3cos 2 x dx If lim f (x) = 7 and g(3) = 4 , then lim ( f (x)g(x)) = 28 . x! 3 x! 3 3. If f (x) is differentiable and concave up for all x, then f (b) " f (a) f !(a) < ;a 0. Then ! 0 1 dx converges for p < 1 and xp ! " a 1 dx xp converges for p > 1. 20. Every continuous function is the derivative of some function. 21. " f (x) ! g(x) dx = ( " f (x) dx )( " g(x) dx ) x 22. ! te t dt = xe x - e x " 3e4 4 t 23. If f is a continuous function and 24. ! (2m 25. The initial value problem 4m - 3 1 dm = +C 3 2 - 3m + 2) "2(2m - 3m + 2)2 2 y = x + ln x ! 1 + a 26. !c f (x) dx = G(t) , then G !(t) = f (t) . dy x + 1 = , y(1) = a has solution dx x If, f is continuous and positive for x > a and lim f (x) = 0 , then x!" ! " f (x) dx converges. a 27. 2 There exists a function F such that F '(x) = e x . 2 MATH 1A/1B REVIEW PROBLEMS 28. Suppose that f (x) and g(x) are differentiable functions. Then, # f !(x)g(x) + f (x)g!(x) & (' dx = ln f (x) " g(x) + C f (x) " g(x) ) %$ 1 29. ! g(x) dx = ln g(x) + C 30. Assume that f is a twice-differentiable function. Then integration by parts b will show that, #0 x ! f ""(x) dx = b ! f "(b) - f (b) + f (0) Use the table below to record your answers as you work through this form. Be sure to ENTER your final answers on a SCANTRON form and submit the SCANTRON on the day listed on the course calendar. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Over, please 3