midterm1

midterm1 - MATH 125 Spring 08 Midterm 1 Name x2 1 x1 x<1...

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MATH 125 Spring 08 – Midterm 1 Name 1. (20 pts) Let f ( x ) = x 2 - 1 x - 1 , x < 1 c, x = 1 5 x + b, x > 1 (a) Find lim x 1 + f ( x ) and lim x 1 - f ( x ), respectively. (b) Find values of b and c for which f is continuous in ( -∞ , ). Sketch the graph of f ( x ). 1

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2. (40 pts) Evaluate the following limits. Write + , -∞ or “Does not exist”, if appropriate. (a) lim x 0 x + 2 - 2 x (b) lim x →∞ ( x - x ) (c) lim x 0 sin x tan x 2 x 2 (d) lim x 0 + ln x 4 + 3 ln x (e) lim x 2 - x 2 - 3 x + 2 sin( | x - 2 | ) 2
3. (40 pts) Let function f ( x ) be given by f ( x ) = x 2 + 1 2 x - 5 . (a) ﬁnd all discontinuous points. (b) specify all vertical asymptotes, if there is any. Show all limit behavior to support your claim on asymptotes. (c) specify all horizontal asymptotes, if there is any. Show all limit behavior to support your claim on asymptotes.

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This note was uploaded on 04/17/2009 for the course MATH 125 taught by Professor Tuffaha during the Spring '07 term at USC.

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midterm1 - MATH 125 Spring 08 Midterm 1 Name x2 1 x1 x<1...

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