praexam2sp10141

# praexam2sp10141 - x x 2 − π 2 4 for 0 ≤ x< π 2...

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Math 141 (Section 04) Practice EXAM 2 1. Let f ( x ) = ln x + x for x 1. a) Justify why f has an inverse and Fnd the domain and the range of f 1 . b) ±ind ( f 1 ) (1) . 2. a) Simplify sec(tan 1 ( x 2 )). b) ±ind f ( x ) if f ( x ) = (1 + 1 x ) x , for x > 0. 3. Evaluate the following integrals a) i π/ 2 0 sin x 16 cos 2 x dx. b) i 4 3 1 x 2 6 x +18 dx. 4. a) ±ind the following limits, justify your answers and clearly identify all indeterminate forms. (i) lim x 0 tan x x sin x x . (ii) lim x 0 + ( x ) sin x . b) Let f ( x ) = cos
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Unformatted text preview: x x 2 − π 2 / 4 for 0 ≤ x < π/ 2. ±ind the value that should be assigned to f ( π/ 2) to make the function f continuous on [0 , π/ 2]. Justify your answer. 5. Consider the following linear Frst order di²erential equation x 2 dy dx + y = 1 , x > . a) ±ind the general solution of the equation. b) ±ind the particular solution for which y (2) = 3. 1...
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