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Math 150a Midterm #3. November 18, 2005
Attention! Please, note that this is the closed book test. You are not allowed to use graphing
calculator. Simple calculators are allowed. Please, show all important steps in you solution but do
not make your solution excessively long.
1. (8pt) Write the expression for the differential of function
f(x) = sin( + x);
(4pt) Use differentials to calculate absolute error for f(x) at x = 0 for dx = 0.03;
(3pt) Use differentials to calculate relative error for f(x) at x = 0 for dx = 0.03.
2
2. Sketch the graph of the function f(x) following the steps listed below:
f(x) = e1x2
 1.
a)(3pt) specify the domain;
b)(5pt) specify the intervals of increasing and decreasing, list critical points;
c)(5pt) specify the intervals where the function is concave up and concave down, list
inflection points;
