APPM 1350 FINAL EXAM SUMMER 2009
On the front of your bluebook write: (1) your name, (2) your student ID number, and (3) a
grading table. You must work all of the problems on the exam. SHOW ALL YOUR WORK in
your bluebook and BOX in your final answers. A correct answer with no relevant work may
receive no credit, while an incorrect answer accompanied by some correct work may receive partial
credit. Text books, class notes, calculators and crib sheets are NOT permitted. Please start each
new problem on a new page of the bluebook.
1. (50 points, 5 points each) For each of the follwing unrelated statements, answer TRUE or
NOT NECESSARILY TRUE.
(a) If f0(x)≥0 for all xand f(0) = 0, the f(x)≥0 for all x.
(b) The function f(t) = sin t
t2has a continuous extension at t= 0.
(c) The derivative of the function csc2xis same as the derivative of cot2x.
(d) Zπ
−π
xsin x
x2+ 1 dx = 0
(e) If fand gare continuous and f(x)≥g(x) for a≤x≤b, then Zb
a
f(x)dx ≥Zb
a
g(x)dx
(f) There exists a function fsuch that f(1) = −2, f(3) = 0, and f0(x)>1 for all x.
(g) If gis continuous and g(5) = 2 and g(4) = 3 then lim
x→2g(4x2−11) = 2.
(h) All continuous functions have derivatives.
(i) All continuous functions have antiderivatives.
(j) The inverse function of y=e3xis y=1
3ln(x)
2. (25 points, 5 points each) Answer each of the following unrelated questions. No partial credit
will be awarded, and no justification is necessary.
(a) Find the average rate of change of a(r) = log10(r2+ 1) on the interval [0,3].
(b) Find the instantaneous rate of change of a(r) = log10(r2+ 1) at t= 3.
(c) Find all critical points of the function h(t) = t+9
t.
(d) Evalutate:
5
X
k=0
sin (2k+ 1)π
2
(e) State the Fundamental Theorem of Calculus, Parts I and II.
THE EXAM IS CONTINUED ON THE BACK
