Math 1271, Summer 2010, Worksheet 2.11. Let f(x) =x4−1√x−1for x 6= 1. Find f(.9), f(.99), f(.999), f (1.1), f(1.01), and f(1.001).Based on this data, what would you guess is the value of the following limit:limx→1x4− 1√x − 1?2. Let f (x) =e2x−1xfor x 6= 0. Find f(.1), f(.01), f (.001), f(.0001), and f (10−5). Basedon this data, what would you guess is the value of the following limit:limx→0e2x− 1x?3. Let f(x) = cos 100πx. Find f(.4904), f(.2503), f (.0902), and f (.0101). Based on thisdata, what would you guess is the value of the following limit:limx→0cos 100πx?In fact, what is limx→0cos 100πx?1Math 1271, Summer 2010, Worksheet 2.21. Find the equation of the line through the two points (-2,12) and (6,-8).2. Consider the parabola which is the graph of the equation y = x2− 3x − 10. Find theequation of the secant line which intersects this parabola at the two points where x = −3and x = 4.3. A particle is moving on a straight line. Its position s on the line at any time t is givenby s = t2− 4t. Find the average velocity of the particle on the time interval 2 ≤ t ≤ 10. Ifyou need to think in terms of units, let s be measured in feet and t in
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