PracticeMidterm1

PracticeMidterm1 - inverse of the function restricted to...

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Math 20A Spring 2008 Practice Midterm 1 Instructor: Oded Yacobi April 15, 2008 Instructions: Turn o/ and put away your cell phones. No notes, calculators, or any other electronic devices are allowed during this exam. Read each question carefully and answer each question completely. Show all your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear ask 20 points. Good luck! 1. Let f ( x ) = 1 =x 2 , h ( x ) = ln( x + 3) + 4 , g ( x ) = ( x 3) 2 . Do the following for each of f; h; and g . a. Find domain and range of the function. b. Sketch the graphs of the function. c. Find the domain on which the function is 1-1 and a formula for the
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Unformatted text preview: inverse of the function restricted to its domain. d. Sketch the graph of the function. 2. Solve for x : log 3 ( x 2 ) & 2 log 3 ( x 3 ) = 1 3. This distance travelled by a particle at time t is s ( t ) = t 2 + 3 t + 1 . Calculate the average velocity over the time interval [1 ; 4] . 4. Evaluate the following limits and justify your steps: a. lim x &! e x & e 2 x 1 & e x b. lim x &! tan 4 x tan 9 x 5. Determine the points at which the function is discontinuous and state the type of discontinuity: removable, jump, in&nite, or none of these: a. f ( x ) = x +1 4 x & 2 b. f ( x ) = [ x ] 1...
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