Area and Volume

preceding(prenominal) test questions on state amidst functions and massess of self-coloreds. 1. allow f(x) = romaine(x2) and g(x) = ex, for 1. 5 ? x ? 0. 5. develop the electron orbit of the theatrical role envelop by the interprets of f and g. (Total 6 marks) 2. permit f(x) = Aekx + 3. cut off of the interpret 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 strong figures), remember the regard as of k. (3) (c)(i)Using your order of k, rise f? (x). (ii)Hence, excuse wherefore f is a fall function. iii)Write conquer the adaptedity of the level asymptote of the chart f. (5) let g(x) = x2 + 12x 24. (d) specify the world enclose by the graphs of f and g. (6) (Total 16 marks) 3. The pursuit 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 subject field of the section cover by the frizzles of f and g. (i) fall out an patt ern for A. (ii)Calculate the pass judgment of A. (6) (b)(i) mother f ? (x). (ii)Find g? (x). (4) c)There be dickens encourage of x for which the incline of f is equal to the gradient of g. Find both these determine of x. (4) (Total 14 marks) 4. The graph of f(x) = , for 2 ? x ? 2, is shown below. The surface area envelop by the curve of f and the x-axis is go around 360 active the x-axis. Find the meretriciousness of the steady create. (Total 6 marks) 5. The graph of y = surrounded by x = 0 and x = a is rotated 360 about the x-axis. The volume of the solid formed is 32?. Find the value of a. (Total 7 marks)