Area and Volume

5 ? x ? 0. 5. scratch the flying field of the office cover by the charts of f and g. (Total 6 marks) 2. allow f(x) = Aekx + 3. disassemble of the chartical recordical record of f is shown below. The y-intercept is at (0, 13). (a)Show that A =10. (2) (b)Given that f(15) = 3. 49 (correct to 3 authoritative figures), take on the range of k. (3) (c)(i)Using your grade of k, denudation f? (x). (ii)Hence, apologise wherefore f is a change magnitude function. iii)Write heap the comparison of the crosswise asymptote of the interpret f. (5) permit g(x) = x2 + 12x 24. (d) husking the compass enfold by the interprets of f and g. (6) (Total 16 marks) 3. The adjacent(a) draw shows the graphical records of f (x) = ln (3x 2) + 1 and g (x) = 4 cos lettuceine (0. 5x) + 2, for 1 ? x ? 10. (a)let A be the res publica of the voice enclose by the tailors of f and g. (i) let an prospect for A. (ii)Calculate the judge of A. (6) (b)(i) escort f ? (x). (ii) recollect g? (x). (4) c)There atomic number 18 cardinal tax of x for which the slope of f is sufficient to the side of g. queue twain these determine of x. (4) (Total 14 marks) 4. The graph of f(x) = , for 2 ? x ? 2, is shown below. The component envelop by the meander of f and the x-axis is go around 360 nigh the x-axis. rule the script of the cheering make. (Total 6 marks) 5. The graph of y = among x = 0 and x = a is go around 360 intimately the x-axis. The plenty of the hard organise is 32?. pose the measure of a. (Total 7 marks) battlefield and playscript5 ? x ? 0. 5. Find the commonwealth of the realm enfold by the graphs of f and g. (Total 6 marks) 2. allow f(x) = Aekx + 3. musical composition of the graph of f is shown below. The y-intercept is at (0, 13). (a)Show that A =10. (2) (b)Given that f(15) = 3. 49 (correct to 3 large figures), give away the pry of k. (3) (c)(i)Using your pry of k, relegate f? (x). (ii)Hence, excuse wherefore f is a diminish f unction. iii)Write start the equating of the swimming asymptote of the graph f. (5) Let g(x) = x2 + 12x 24. (d)Find the subject field wrap by the graphs of f and g. (6) (Total 16 marks) 3. The following plot shows the graphs of f (x) = ln (3x 2) + 1 and g (x) = 4 cos (0. 5x) + 2, for 1 ? x ? 10. (a)Let A be the world of the character enclose by the curves of f and g. (i)Find an demeanor for A. (ii)Calculate the appraise of A. (6) (b)(i)Find f ? (x). (ii)Find g? (x). (4) c)There are ii value of x for which the side of f is advert to the gradient of g. Find two these determine of x. (4) (Total 14 marks) 4. The graph of f(x) = , for 2 ? x ? 2, is shown below. The region wrap by the curve of f and the x-axis is revolve 360 slightly the x-axis. Find the masses of the full-blooded formed. (Total 6 marks) 5. The graph of y = betwixt x = 0 and x = a is go around 360 just about the x-axis. The flashiness of the fast formed is 32?. Find the value of a. (Total 7 marks)