REVIEW FOR TEST 1
You should be able to:
-  find the limits of a function at a point and at infinity, given its graph
- compute limits of functions at a point and at infinity
- determine whether a function is continuous at a point or on an interval
- find the discontinuity points for a given function
- use the Squeezing Theorem to show that a certain limit has a specific value


Exercises to Practice:
page 128: # 1, 5-17, 31a, 32a, 33
page 77: # 5, 7, 9, 22, 25
page 87: # 12, 13, 25, 27, 32, 38
page 97: # 3,5, 18, 25, 29, 35, 37, 59, 60
page 118: #  1, 15,21, 30, 35, 39
page 126: # 23, 27, 29, 33,34, 39
Page 127: 68a
Use the squeezing Theorem to show that the lim(x sin(1/square root of x)) when x goes to 0+ is 0

REVIEW FOR TEST 2

You should be able to:
- state the Intermediate Value Theorem (p. 115)
- state the definition of the derivative as it appears on page 143 in the textbook
 - use the Intermediate Value Theorem to show that an equation has at least one solution on the given interval
- Compute the derivative of a function using the definition (Definition 2.2.1)
- Compute the derivative using the rules of differentiations and formulas
- Find the slope of  the tangent line to the graph of a function  and write an equation of the tangent line
- Find the points on the graph at which the tangent line has special properties (is horizontal, parallel/perpendicular toa given line)
- Compute higher order derivatives


Exercises to Practice:
Page 127: # 67a
Page 152: # 10, 13
Page 154: # 47
Page 161: # 13,41d, 44b
Page 168: # 7, 8, 13, 29,31, 32, 33
Page 172: # 13, 21, 26, 29b,
Page 179:# 27-40, 45, 54
Page 183: # 9, 26, 28, 29-34, 37,39, 41

REVIEW FOR TEST 3

You should be able to:

- Compute the derivative of a piecewise function at the point where formulas change (“breaking” points)
- Determine whether a function is differentiable at a point (using the definition or the graph)
- Find the average rate of change  and the instantaneous rate of change
- Find the average and instantaneous velocity of a particle moving on a straight light; find the total distance traveled (see quiz # 4)
- Compute the derivative of a function given implicitly
- Compute the derivative of a function containg and exponential, logarithmic and inverse trig functions
- Use logarithmic differentiation
- Solve a related rate problems
- Write the local linear approximation of a function at a given value of x
- Use local linear approximation to approximate values of functions
- Compute differential of a function




Exercises to practice:
Page 162: # 66, 67
Page 196: # 20, 25, 28,37
Page 217: # 17 (+ use the approximation to find square root of 3.2 skip the graphing calculator part),  45, 51
Page 229: # 5, 8,  9, 10, 15-36, 59,61,  62
page 209: # 14, 17, 25, 25
Page 202: # 26, 30, 34, 45, 48


REVIEW FOR TEST 4
You should be able to:
- Use differentials to approximate change in values of y (delta y) and propagated errors
- Use l'Hopital rule to evaluate limits (0/0, infinity/infinity, 0.infinity)
- Evaluate limits of the form infinity-infinity, 0^0, infinity^0, 1^infinity
- Find intervals on which a function is increasing/decreasing/concave up/concave down
- Find critical points, identify relative extrema, identify  inflection points
- Use the First Derivative Tests to determine existence of relative extrema
- Graph a function by following steps discussed in class


Exercises to Practice:
Page 218: # 53, 61
Page 226: # 7, 15, 17, 19, 21, 23, 25
Page 227: # 27-43
Page 310: #3-9, 14, 24-27 ,29, 33 43, 44
Page 242: # 25, 29, 33
Page 264: # 3, 35, 45, 57

REVIEW FOR TEST 5
You should be able to:
- Use the Second Derivative Tests to determine existence of relative extrema
- Find the absolute extrema of a continuous function on a closed interval
-Find the absolute extrema of a function
- Solve optimization problems
- Check whether the hypothesis of Rolle's and Mean Value Theorems are satisfied and find value(s) of c from the conclusion of these theorems
- Evaluate integrals by using formulas and the substitution method.

Exercises to Practice:
Page 310: # 55, 56, 63, 75
Page 284: # 11, 21, 23, 31
Page 308: # 3, 7,
Page 338: # 19, 25, 31, 35, 45, 53
REVIEW FOR THE FINAL
Review