Wednesday, March 4
Clicker Questions
Clicker Question 1
Applying the Squeeze Theorem
(−1)n + 2n + 3 cos 4n
.
n→∞
n
Calculate lim
A. 0
Two bounding sequences
B. 1
Since (−1)n is either −1 or 1, and 3 cos 4n is
always between −3 and 3, the limit must lie
between
2n − 4
2n + 4
lim
and lim
,
n→∞
n→∞
n
n
both of which equal 2.
C. 2
D. 3
E. 4
Clicker Question 2
Will this problem send you to the hospital?
ln n
.
n→∞ n1/9
Evaluate lim
A. converges to 9
Using l’Hôpital’s Rule
B. diverges
It suffices to calculate limx→∞ xln1/9x ,
which is an ∞
∞ indeterminate form. Its
limit is therefore equal to
C. converges to 1/9
D. converges to 1
E. converges to 0
1/x
(ln x)0
= lim −8/9
1/9
0
x→∞ (x
x→∞ x
)
/9
9
= lim 1/9 = 0.
x→∞ x
lim