Assignment II∗Sayyid Mohammed HasanFebruary 14, 2014∗ Lastdate for submission 3 March 2014, within class timings.1Prob 1Find the intervals in which f (x) =|x−2|x2is strictly increasing and strictly decreasing.Prob 2Evaluate the limit:limn→∞1sec2n21n2+2sec2n24n2+ ... +1sec2 1nProb 3Find the Integral:sin8 x − cos8 xdx1 − 2 sin2 x cos2 xProb 4Discuss the Application and conclusion of Lagranges’s Mean Value Theorem on the function f (x) = |x| oninterval [−1, 1].Prob 5If y = sin−1 x + sin−1√1 − x2 then finddydx .Prob 6Find the value of log3 log3 log9 729 + 3 log√3 3.Prob 7Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 ≤ x ≤ 2π/3.Prob 8Find the minimum value of f (x) =x2 −x+1x2 +x+1 .Prob 9For what values of a and blimx→∞x2 + 1− ax − bx+1= 0.Prob 10Find the Integral:12x3 2 + x314dx***********END**********1

A YOGANJANEYULU , 11 Years ago

Grade 11