Part B TIME: 60 MINUTES
No calculator is allowed for any of these problems.
If you finish Part B before time has expired, you may return to work on Part A, but you may not
use a calculator.
- The graph of function y = f (x) passes through point (2, 5) and satisfies the differential equation
(a) Write an equation of the line tangent to f at (2, 5).
(b) Using this tangent line, estimate f (2.1).
(c) Solve the differential equation, expressing f as a function of x.
(d) Using your answer to part (c), find f (2.1).- Let R represent the first-quadrant region bounded by the y-axis and the curves y = 2x and
as shown in the graph.
(a) Find the area of region R.
(b) Set up, but do not evaluate, integrals in terms of a single variable for:
(i) the volume of the solid formed when R is rotated around the x-axis,
(ii) the volume of the solid whose base is R, if all cross sections in planes perpendicular to the
x-axis are squares.