MATH 114 Midterm: MATH 114 UPenn m114 sExam 1 Exam
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Math 114 sample final exam 1: a curve is given in parametric form by x = et2. Its tangent line at the point (1,0) is (a) y = 3. 2 (b) y = x + 1 (c) y = 2. V3 = ( 1/2, 3/2, 0) and v4 = (0, 0, 2). + y2 = 2 is (b) 12 (c) 9 (d) 9 (e) 0: let s be the square in the xy-plane with vertices (0,2), (0,3), (1,2), and (1,3). 2x cos y da. (c) 2 /3 (d) 17/6 (e) 1 cos 1. (a) 0 (b) 1 + 2: evaluate (cid:1) 2 (cid:1) y cos(x2) dxdy. (a) 1/2 (b) 1 (c) (d) (cid:2) /2 (e) 2: let d be the region d = {(x, y)|x2 + y2 1, x 0, y 0}. Compute (cid:1) (cid:1) (cid:1)d exp(cid:3)(x2 + y2 + z2) 2(cid:4) dv. (here exp is the usual exponential function, i. e. , exp(x) = ex). (a)
