praexam2sp10141

praexam2sp10141 - x x 2 2 / 4 for 0 x < / 2. ind...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x x 2 2 / 4 for 0 x < / 2. ind the value that should be assigned to f ( / 2) to make the function f continuous on [0 , / 2]. Justify your answer. 5. Consider the following linear Frst order dierential 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...
View Full Document

Ask a homework question - tutors are online