Solve them plz
102.2. EXERCISES (16) The intervals on which the function f(r) = 1 + is increasing are ( - : - ) and (17) Consider the function for zer. (a) The intervals on which f is decreasing are (_ ) and ( (b) How many local maxima does f have? Answer: (c) The interval on which f is concave up is (_ (18) Consider the function f : r. rexp(-4z?). (a) The intervals on which f is decreasing are ( ) and ( (b) The intervals on which f is concave up are (-a, 0) and (a , co ) where a = (c) f has how many points of inflection? Answer: _ (19) Consider the function f: r. In(4 -r?). (a) The domain of f is the interval ( (b) The interval on which f is increasing is (c) f is concave (20) Consider the function for rinr. (a) The domain of f is the interval (. (b) Im S(x) = (c) The interval on which f is positive is ( (d) The interval on which f is increasing is ( (e) The function f attains its minimum value of -- at x = where a = and b= (f) f is concave (21) Consider the function forur Ir. (a) The domain of f is the interval (_ (b) lim / (s) = (c) The interval on which f is positive is (. (d) The interval on which f is increasing is ( (e) The function f attains its minimum value of - at 1= where a = and b= (f) f has a point of inflection at a = el where p = (22) Consider the function f: 1. r(lar) (a) The domain of f is the interval ( (b) lim f(x) =. (c) The intervals on which f is increasing are (0, 2 ), where a = _ - , and (d) The function f attains its minimum value of at 1 = (e) f has a point of inflection at r = el where p = 10. MONOTOXICITY AND CONCAVITY (23) Consider the function fire - Inr. (a) The domain of f is the interval ( (b) lim f(x) = (c) The interval on which f is increasing is (_ (d) The function f attains its maximum value of at 1 =. (e) f has a point of inflection at r = el where p = (24) Let f(x) = e sina for 0 3 (a) Is it possible to define f at r = 0 in such a way that f becomes continuous at r = (? Answer: . If so, then we should set f (0) = (b) Is it possible to define f at r = 1 in such a way that f becomes continuous at r = 1? Answer: If so, then we should set / (1) = _ (c) Is it possible to define f at r = 3 in such a way that f becomes continuous at r = 3? Answer: If so, then we should set f (3) = r+4 if r 3 (a) Is it possible to define f at r = -2 in such a way that f becomes continuous at r = -27 Answer: . If so, then we should set f (-2) = (b) Is it possible to define f at r = 1 in such a way that f becomes continuous at r = 1? Answer: .. If so, then we should set f (1) = _ (c) Is it possible to define f at r = 3 in such a way that f becomes continuous at r = 37 Answer: If so, then we should set f (3) = _ (4) The equation r + r + 2r = 2r + 3r- + 4 has a solution in the open interval (n, n + 1) where n is the positive integer (5) The equation r'-6r--53 = 22r-2r has a solution in the open interval (n, n + 1) where n is the positive integer (6) The equation ' + r + 1 = 3r + r has solutions in the open intervals (m, m + 1) and (n, n + 1) where m and a are the distinct positive integers and (7) The equation m' + 8r = 2r + 6r- has solutions in the open intervals (m, m + 1) and (n, n + 1) where m and a are the distinct positive integers and101. Consider the following statements related to the RBI: 1. Reserve Bank of India was privately owned before its nationalistaion. 2. After nationalization the RBI seized to function as a bank. 3. Now RBI does not subscribe to the primary issue of the G-Secs. Which of the above is/are not correct? (a) Only 1 (b) 1 and 2 (c) Only 3 (d) None of the above(37) Find when y = (sing )and for 0
