Find the derivative and simplify: = ^tan .

Find the derivative of the function () = ( + 1/) and simplify your answer as far as possible.

limit problems using derivatives; do not use that method here but use only some algebra instead, and limits, such as lim 0 sin ()/ = 1, for example, where A is any real quantity assumed measured in radians.)

L1. Find the limit lim 0 ||/ if it exists. If you say that it does not exist, say why not. Hint: Deal separately with the two one-sided limits.

L2. Find the limit lim 0 |sin |/ if it exists. If you say that it does not exist, say why not.

L 45. Use "rationalizing" to find the limit lim 0 sin (4) /1 1 .

L 40. Find the limit lim /2 2 . Here, an and b are real numbers with a > b, so that a - b > 0. (Your answer will involve both a and b.)

L 42. If () = {^2 + 2, 1

2 + 1, < 1 , then lim 1 () A. is 1 B. is 2 C. is 3 D. Does not exist.

L4. Evaluate the limit lim (2 + 1)^40 (4 1)^5/(2 + 1)^45 .

C1. If () = {^4 16 / 2 , 2 16, = 2 , Which of the following is true: A. f is continuous at x = 2. B. f is discontinuous at x = 2. C. lim 2 () = 16. D. None of these. As usual, show the work that leads to your choice.