1. Consider the position function s(t) = sint representing the position of an object moving along a line on the end of a spring. Sketch a graph of s together with a secant line passing through (0, s(0)) and (0.5, s(0.5)). Determine the slope of the secant line and explain its relationship to the moving object. 2. Sketch a graph of f and use it to make a conjecture about the values of f(a), lim f(x), lim f(x) and lim f(x) or state that they don not exist. xa xa+ xa 3-x if x < 2 (x) = { x-1 if x > 2; a = 2 *** Use analytical methods for Question 3, 4 and 5. 3. Find the following limit or state that they do not exist. lim x3 1 x+2x 4. Evaluate the limit. Do not use L'Hpital's Rule. 15 13+) x - 3 3x-1 lim x1 x-1 5. Analyze the following limits and find the vertical asymptotes of f(x) a. lim f(x) b. lim f(x) c. lim f(x) d. lim f(x) x7- x7+ x7 x0 = x + 7 x4 - 49x