Be sure to show all of your work. All solutions should use calculus techniques from this course. You may only use the formula sheet and scratch paper supplied with this exam. 2: lim x 2, find the following limits (5 points each), giving reasons for your answers. You may use any method from this course. x + 2 x2 2x. 2 x sin(5x) 5x x3: lim x 0, find the derivatives of the following functions (7 points each). You do not need to simplify your answers. 3: if y = tan(3x2 + e) then dy dx, if y = e x x+1 then dy dx, find the following inde nite integrals (7 points each). 4 a. (cid:90) t2 cos(1 t3) dt = (cid:90) b. x 1 dx : calculate the following de nite integrals (7 points each). a. dx = (cid:90) 3 ln(x) x. 1 b. x 1 dx = x.