Rex Wu S22M171 Assignment PQ Exam1_Optional due 03/01/2022 at 11:59pm MST [?/A/B/C/D] Speeding up 1. (1 point) Which graph has the property: For all x, the average rate of [?/A/B/C/D] Speeding up and then slowing down change over the interval [0, x] is greater than the instantaneous rate of change at x. [?/A/B/C/D] Slowing down [?/A/B/C/D] Slowing down and then speeding up (A) (C) (D) Answer(s) submitted: (incorrect) 3. (1 point) Find the average rate of change of the function f(x) = sin(x) (B) over the interval 0 /=] the rate of decline at 1 = 16? (b) Draw the secant line whose slope is the average rate of change in infected children over the interval [0,4] (c) Estimate AN on the interval [0,6]. What are the units of At . days percent infected percent infected per day Atx = 1, the function is . days per percent infected (d) Using the formula for N(t), compute lim N(t). . left-continuous right-continuous Answer(s) submitted: neither At x = 3, the function is . left-continuous (incorrect) right-continuous 6. (1 point) . neither Determine the one-sided limits at c = 1,2, 3 for the function Atx =5, the function is f shown in the figure and state whether the limit exists at theses . ? points. . left-continuous . right-continuous . neither 5 - y = f (x ) Answer(s) submitted: (incorrect) 5. (1 point) (a) lim f(x) = An epidemiologist finds that the percentage N(t) of suscep 1 1- tible children who were infected on day t during a measles out- (b) lim f(x) = break is given, to a reasonable approximation, by the formula: (c) lim f(x) = 10012 N(1) = 73+5+2 -1001+380 d) lim f(x) = x -+2+(e) lim f(x) = * +3 - (f) lim f(x) = (g) Does the limit exist at c = 1? [?/Yes/No] (incorrect) (h) Does the limit exist at c = 2? [?/Yes/No] (i) Does the limit exist at c = 3? [?/Yes/No] 9. (1 point) Answer(s) submitted: For each limit, evaluate the limit or or explain why it does not exist. (1) lim _2 * $2x2-4 x - 2 (2) lim x -+2 . . . (3) lim x -+0+ Vx Vx2+ x (e" + 4e-51 (4) lim 1-40 el - (incorrect) x2 - 16 (5) lim - x 14 V x - 2 7. (1 point) (2+x) 2 - 4 Given lim f(x) = 5 and lim g(x) = 2, use limit laws to com- (6) lim * + 2 x -+0 pute the following limits or type "indeterminant" if you cannot find the limit. Answer(s) submitted: (1). lim (2f(x) -8(x)) = (2). lim (f(x)8(2)) =_ X -+ 2 (3). lim (x)8(x) . . * + 2 (4). lim (f (x) 2 + x- 8(x)2 = * + 2 (5). lim (f (x) ) 3/2 = * + 2 (incorrect) (6). lim (x)-5 *-+28 ( 1) - 2 Answer(s) submitted: 10. (1 point) Let g be a function such that, for all real numbers x near 5 but not equal to 5: . . 4 cos ( x - 5) 1 (incorrect) exists. C = (2) Is there a number c such that f(x) is continuous at x = 1? 11. (1 point) [?/Yes/No] Justify your answer. What does the Squeeze Theorem say about lim f(x) if lim I(x) = lim u(x) =6 and f(x), u(x), and I(x) are related to * +7 the figure ? Answer(s) submitted;f(.x) 13. (1 point) The following identity may be useful: cos(x+ y) = cos(x) cos(y) - sin(x) sin(x) Simplify and compute the limit lim cos(x +h) - cos(x) 1( x ) h-+0 1(.x) Answer(s) submitted: lim f(x) = (incorrect) 14. (1 point) The inequality f(x)