Question 2A

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1. Find the average rate of change of the function f (x) = x + 2x3 + 1 on the interval [1, 3] 2. Calculate lim r' - 5r + 6 |x - 21 3. Find all horizontal asymptotes of the curve y = r + 5r+l V16r + 3x + 7 4. Calculate lim 145 x -7x + 10 5. Find possible formulas for f(x) and g(x) such that lim f(z) = lim g(x) = 0 and I-130 I-+00 lim f(x) =2. DO g(I) 6. Find possible formulas for k(x) and /(x] such that lim k(x) = lim I(x) = 0 and k(I) lim -00. 7. If lim f(x) = 5, then find lim 8. If lim 9(2) + 1 = 5, then find lim g(x). 9. Consider the function if x 5 -2 -2x + 3 if - 2 10 (a) Determine the value(s) of a such that lim f(z) does not exist. (b) Determine the value(s) of b such that f is not continuous at a = b. 10. Calculate lim arctan 11. If lim f(x) = lim g(x) = co, then what is lim (f(2) - 9(x) )? If it is impossible to tell with only this information, explain why