MATH 101 Final, Fall 2001

1. 2. 3. 4. 5. 6. Math 101 Final Exam January 31, 2002 Let f: R— Abe given by f(x) = x — 2X - 2x. (i) Sketch the graph of f. (ii) Find the area of the region enclosed by the curve y = (x) and the straight line y= x. Find the volume generated by revolving about the X-axis the region given by the curve y= sinx and the interval O< x<n. The region bounded by the curve y = ¥ + 1 and the line y = -x + 3 is revolved about the X~ axis. Find the volume generated. Xx Let f: R-» Abe given by fx) = ae Vv i) Find the intervals of R on which fis increasing; ( (ii) Find the intervals of R on which fis decreasing; ( ( iii) Locate the points of local minima and local maxima; iv) Find the intervals of R on which the graph of fis concave up and concave down; (v) Locate the points of inflection of the graph of f Find the equation of the tangent line to the curve xsin2y — ycos2x = O at the point (x/4, n/2) Evatuate the following limits : i) limsec(xsec*x - tan*x - 1); (i), fim 2x—tan’x-14 (ii) yr +7x-25 im >: vee Suv — 7a +25