MATH 101 Questions, Fall 2013

Time: 60 minutes 26/11/02 MATH 101 Sections 5, 6, 7,8 Quiz I First Semester, 02-03 Instruction: Show your work in all the problems. 1.Given f(x) =x, g(x) = V1-x. Find g(f(x)) and find its domain and range. 2. (a) Find the points of discontinuity for the function f(x), whose graph is given below. For each such point, explain why the function is discontinuous there. (b) If possible, remove one discontinuity by assigning a different value for the function at that x. Explain. 3.Use reference triangles to find each of the following: 6 (a)csc'(-2) (b) sec (cot 1) (c) tan (sin'x), x> 0 x #0 4. f(x) = 0, x=0 (a) Find jm f(x) and lim f(®) -Does Lim £09 exist? Explain. x30" x0” x40 (b) Is (x) continuous at 0? Justify your answer. . . vx+2-2 6. Find Jimmy x2 6. Given g(x) === ; x (a) Find horizontal and vertical asymptotes of the graph of g(x) from the function rule._Do not draw the graph. (b) Find Jim — imGog ( Show your work. 7. Given the function f(x) = -2x2, Find the slope m of the curve of f{x) at x =3. (Use the limit definition of m) Tran we EER weeds 8S LEU RAR Y re EERO a epee me