BEWARE! When plugging c into a function, if - is obtained, STOP, no conclusions can be drawn. This is called indeterminate form. The best way to deal with indeterminate form is to use algebraic simplification (such as factoring and cancellation). 3. 2x2-3x-2 Find lim x-1 x2+x-1 4. Find lim x2+4x+3 x- -3 x+3 5. Piecewise Limits Let f (x) = Sx2 + 1 ifx 2 a) Find lim f (x) b) Find lim f (x) x-2- c) Find lim f (x) x - 2+ x-2 d) Find f (2) Infinite Limits Consider the function: f (x) = = x2+20 What is lim x2 + 20 , What is lim x2 +20 5 ( x - 2 ) 2 X -2+5(x-2)2 X-2 - 5(x-2)2 - What can we say about lim +20, x-2 5(x-2)2 - X f (x ) = x2 + 20 x2 + 20 5 (x - 2) 2 X f ( x) = = 5 (x - 2) 2 f(x) 2.1 10 1.9 10 2.01 100 1.99 100 f(x) = x2 +20 2.001 1000 1.999 1000 5(x - 2)2 This table shows the value This table shows the value f(x) tends to as x approaches f(x) tends to as x approaches 2 from the right. 2 from the left. 6. Find the left-sided, right-sided, and two-sided limit as x approaches 1 of f (x) =; (x -1) 2