You may use a calculator, but no books or notes. Note that the take-home problem is worth 12 points. take home. Evaluate the limits. (a) lim t 2 t2 t 2 t2 4 (b) lim x sin(x) x (c) lim x 3 . If an object moves with velocity v = , approximate the distance traveled between t = 0 and t = 2 seconds using the left endpoint method with 4 subintervals. page 2 (15) 3. A window in the shape of a rectangle topped by a semicircle has a perimeter of 12 feet. Find the dimensions of the window of largest area. Apply the second derivative test to con rm that your answer is a local maximum. (14) 4. Do not simplify. (a) y = x2 cos2(5x) page 3 (b) x = r t t2 1 (10) 5. Find an equation for the tangent line at x = 0 to the curve y = x2 + 1.
