Sketch the graph of a function y − f(2) such that all of the following statements are true: - • lim_ f(x) — −2 1+0+ lim f(x)-1 1+0 • f(0) - -1 ⚫lim f(x) - co 2 lim f(x) - 1+2+ --∞ H NW 2 3 6 5 4 -6 - 5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 -5 -6 20 5 6 7

solve for lim

Find 2-Vx2-5 lim X→1 x+3

x* + x² - 1 =) Find lim

( 3x +2 x² + 3x – 1 x -2

Sketch the graph that satisfies all of the given conditions. f(2) = 0 f(x) 2 f(x)>0 when x 0 when x 3 xX lim f (a) = 2 and lim fx -2 xx In the box below, write the interval of increase for f.

3x* - 4x +1 lim P) (x-1)2

Use the graph of f(x) = X (x²+2x-8) ² 10 Ay 8- 6- 4 -10-8-6-4-2 2- -2 -4. -6- -8- -10 to determine lim f(x) and lim f(x). X→-4 X→2 2 y = f(x) X 4 6 8 10 Q

The function h is defined by h(x) = ². Which of the x²_ X- -9 x-4 following statements must be true? A B (C) D lim h(x) = − ∞ and lim h(x) x→4- x 4+ lim h(x) x→4- lim h(x) x→4- = +∞ and lim h(x) x 4+ = = = and lim h(x) = +∞ x 4+ lim h(x) = +∞o and lim h(x) = +∞ x 4- x 4+

If f is C2 on an interval prove that lim h-0 f(x + h) – 2f(x) + f(x - h) h2 = f" (x). The expression f(x+h) – 2f (x)+ f(x-h) is called the symmetric second difference.