101-2005&2006-3-M10-June2006

101-2005&2006-3-M10-June2006 - (3 Points) b) Find...

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

View Full Document Right Arrow Icon
Kuwait University Math. Compo SeL Dept. Math 101 First Exam June 28, 2006 Time: 90 min. Calculators and Mobile Phones are not allowed. 1. Evaluate each of the following limits, if it exists: x-I a) lim ~ f3-= x-rl V 2x - v,) - x sinx b) lim ~+ ·xm2 X-rO V xv -r 2. Use the E, () definition of limit to show that: lim(5-2x) = 1. x-r2 3. Let f(x) = (x2 - 2x + l)lxl (x2-1)x . (3 Points) (3 Points) (3 Points) a) Find all points of dicontinuity of f and classify each discontinuity as removable, infinite, or a jump.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (3 Points) b) Find the vertical and horizontal asymptotes for the graph of f, (if any). (3 Points) 4. Show that the equation x5 + 2x-5 = 0 has at least one real root. 5. Assume lim f (x) exists and . x-r-l x2 + x-2 f (x) x2 + 2x-1----<---<----x + 3-(x-1)2 -x + 3 . Find lim f(x). x-r-l 6. Let f(x) = (x2-1) sec(~) + tan(x3-1). Find f'(x) (3 Points) (4 Points) (3 Points)...
View Full Document

Ask a homework question - tutors are online