Assigned work: #5,6,7,10,11ac,12,13,14 Definition of a Limit (know this): Limit of a function is the value of the function (y coordinate) as x approaches some specific value. (Note: it doesn’t matter if the function actually gets there..maybe there’s a hole there instead of a function value) S. Evans

1.4 Limit of a Function Example: As x 2 (from both left & right) f(x) 3 Notation: S. Evans

1.4 Limit of a Function Left and Right Hand Limits: y Example 1: 2 1 1x Left:Right: S. Evans

1.4 Limit of a Function By definition a Limit exists if and only if: 1) Both Left Hand and Right Hand limits exist. 2) LHL = RHL i.e. IF and only IF: AND * Remember that f(a) does not necessarily have to equal L. S. Evans

1.4 Limit of a Function Ex. 2: Given: Find: a) b) c) d) Graphically: a) 9b) 0 c) 47 d) Does Not Exist S. Evans

1.4 Limit of a Function Ex. 3: Given: Find: a) b) c) d) a) 2 b) 2 c) 2 d) Does Not Exist S. Evans

1.4 Limit of a Function Ex. 4: Evaluate: a) b) c) (Note: Limits are often easy to evaluate, just sub in the # and see what happens as in Ex. 4 above) BUT BE CAREFUL (of indeterminant and square roots)!!!! See Ex. 5 on next slide. a) 4 b) 0 c) DNE (LHL RHL) S. Evans

1.4 Limit of a Function Ex. 5: Evaluate: a) b) a)Note if you sub in 2 you get an indeterminant form. Try factoring, then solve. b) Note if you sub in 3 you get 0 BUT watch out with square roots. Check if LHL = RHL. Also look at its graph. What do you find now? S. Evans