MATH 105 FINAL EXAM April 13, 2010
Your grade is based on correctness, completeness, and clarity on each
exercise. You may use a calculator, but no notes, books, or other students.
1.) (15 pts.) Compute the following derivatives, using any valid techniques you like. (Be
sure to show enough steps so that it is clear which techniques you are using.)
a.) (5 pts.) f(x) = √π+extan x
b.) (5 pts.) p(t) = 1
1 + t2
c.) (5 pts.) y=xcos x
2.) (15 pts.) Consider the integral Z2
(−x+ 1) dx.
a.) (5 pts.) Interpret the integral as “area under a curve”. Draw the graph with area
shaded in, and use geometry to compute the signed area.
b.) (5 pts.) Evaluate the integral using the Fundamental Theorem of Calculus.
c.) (5 pts.) Are your answers the same or diﬀerent? Explain why your answers should, or
should not, be the same.