MATH 3B Midterm: Math 3B Exam 11
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Try to answer the following questions without the use of book, notes or calculator. Time yourself and try to nish the test in less than 3 hours: let g(x) = z x2 sin x et2 dt. 0 r(5x) dx = 6: find z . Y y3 + 1 dy. (hint: you do not need to know that y3 + 1 = (y + 1)(y2. Y + 1). : (a) use substition to show that for a function f (x) that. 0 f (x) f (x) + f (a x) dx = z a. 0 f (a x) f (x) + f (a x) dx. (b) show that. 0 g(x) dx = 1 (hint: r a (c) find z /2. 1 + tan x f (x) + f (a x) 0 g(x) dx + r a dx. (hint: sin x = cos ( f (x) dx = 1 ex + 1 dx: consider the autonomous di erential equation.
