Mathematics 133 – Intensive Calculus for Science 1 Quiz 4 – October 7, 2005

Your Name:

Do all work on this sheet (front and back if needed). You have 20 minutes. Calculators allowed on this quiz.

A) From the graph y = f(x), determine lim_{x→2^{+}} f(x) and lim_{x→2^{−}} f(x). Is f(x) continuous at x = 2?

B) Fill in this table for f(x) = \frac{x}{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→0^{+}} \frac{x}{sin(5x)}.

x  .2  .1  .01  .001_{\frac{x}{sin(5x)}}

C) Using algebra, determine lim_{h→0} \frac{(2+h)^{2}−4}{h}.