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Using the graph given below, state the value of lim f(c). 23 у. 4 2 0 2 4 If the value does not exist, enter DNE.

6 6 | y = f(x) | 5 --- | ! 1 1 4 4- 1 3 | 1 |-- | 1 X 十 8 0 1 2 3 4 5 6 7 9 Enter each answer as a whole number or a fraction, or DNE for Does Not Exist or undefined. (x)-2 lim +3+ f(x+1) lim 42 (f(r) +2)= -- lim hs) (8 + h) - (8) h

= A function f(x) is said to have a jump discontinuity at x = a if: 1. lim f(x) exists. 1 → 2. lim f(x) exists. 1+a+ 3. The left and right limits are not equal. = 2 I +7 8.0 1 if : <7 Let f(x) = if <> 7 Show that f(x) has a jump discontinuity at x = 7 by calculating the limits from the left and right at = 7 lim f(x) = = I →7 = lim f(x) = 1+7+ Now for fun, try to graph f(x).

Determine the set of x-values where f(1) = 14 2 + 10 + 5x is continuous, using interval notation.

= 20, let e > 0 be arbitrary. Choose 8 = min In formally proving that lim (x² + x) Determine m. in . 1). 1 中T m m =