Q SCI 291: Analysis for Biologists I Prof. Steve Scherba, Jr. Winter, 2023 REVIEW ASSIGNMENT #2 1. (20 Points) (True or False). In each of the following ten (10) questions, clearly answer either "T" for true or "F" for false, then circle that choice. You must justify your answer either mathematically or in well written English sentences, whichever is most appropriate. If the statement is false, then a counterexample will be sufficient to prove it false. a. (21 Points) The lim f(x) depends on how f(a) is defined. b. (2 Points) If lim f(x) =0 and limg(x) =0, then lim / (20) must exist. c. (2 Points) If f(x) = * -4 (x-2) and g (x) = x +2, then we can say that (x) and g(x) are identical functions. d. (2 Points) If lim /(x) =co and lim g(x) =co , then lim [/(x)-g(x)]=0. e. (2 Points) If f(x) =x3, then f(0) exists. f. (2 Points) The function f(x) =(x| has a derivative at x=0. g- (2 Points) d In(@)_1 dx h. (2 Points) For a constant, c, and a function, f(x), derivative of a constant times a function is def (x) _ df (x) dx dx -and the product rule gives def (x) f (20) + f (x) 3x dx doc Hence, the two rules do not agree. dx i. (2 Points) If f*(a)=0, then f has an inflection point at a . 2 Q SCI 291: Analysis for Biologists I Prof. Steve Scherba, Jr. Winter, 2023 REVIEW ASSIGNMENT #2 j. (2 Points) If f(x, y)= x +xy) -2y' , then foxy(x, y) + foxx(x, y)