_____________________________________________________________
Calculus I                                         Quiz 4                        September 29, 2004

Name _________________        R. Hammack                              Score_____
_____________________________________________________________

Find the limits.

(1)   Underscript[lim , x8] (x - 8)/(x^2 - 7x - 8) =Underscript[lim , x8] (x - 8)/((x - 8) (x + 1)) = Underscript[lim , x8] 1/(x + 1) = 1/9


(2)    Underscript[lim , x9] (3 - x^(1/2))/(x - 9) =    Underscript[lim , x9] (3 - x^(1/2))/(x - 9) (3 + x^(1/2))/(3 + x^(1 ... ((x - 9) (3 + x^(1/2))) = Underscript[lim , x9] -1/(3 + x^(1/2)) = -1/(3 + 9^(1/2)) = -1/6


(3)    Underscript[lim , x4^-] 1/(|   4 - x |) =∞  (because denominator approaches 0, and is positive, while numerator is 1)



(4)  This problem concerns the function f(x) = {1 -           if x<0 x 3 - x      if  x≥0

(a)    Underscript[lim , x0^+]   f(x) =Underscript[lim , x0^+] ( 3 - x ) = 3


(b)    Underscript[lim , x0^-]   f(x) =Underscript[lim , x0^-]   1/x = -∞


(c)    Underscript[lim , x0]   f(x) = D.N.E. becuase left- and right-hand limits don't agree.


(d)  Does f  have any vertical or horizontal asymptotes? If so, state them.

Line x=0 is a vertical asymptpote by part (b) above.
Line y=0 is a horizontal asymptote since   Underscript[lim , x -∞]   f(x) = Underscript[lim , x -∞]     1/x = 0