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\leftline{Mathematics 133 -- Intensive Calculus for Science 1}
\leftline{Quiz 4 -- October 7, 2005}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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Do all work on this sheet (front and back if needed).  You have 20 minutes.
{\bf Calculators allowed on this quiz}.
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A)   From the graph $y = f(x)$, determine $\lim_{x\to 2^+} f(x)$ 
and $\lim_{x\to 2^-} f(x)$.  Is $f(x)$ continuous at $x = 2$?
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B)  Fill in this table for $f(x) = {x\over \sin(5x)}$ -- give values
to rounded to 5 decimal places. (Be sure to 
set your calculator in radian mode!)  Use your values to make a 
conjecture about  $\lim_{x\to 0^+} {x\over \sin(5x)}$.
$$\matrix{ x & .2 & .1 & .01 & .001\cr
       {x\over \sin(5x)} & \qquad\qquad &\qquad\qquad  &\qquad\qquad  &\qquad\qquad  \cr
   }$$  
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C)  Using algebra, determine $\lim_{h\to 0} {(2+h)^2 - 4\over h}$.
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