Monday, January 12
Clicker Questions
Clicker Question 1
3
Z
x
Define g(x) =
2
f (t) dt, where
−2
y= f HtL
1
f (t) is the function to the right.
-2
1
-1
2
3
-1
“Net area so far” function
Between x = −2 and x = 3: on what interval, if any, is g(x) flat?
On what interval is g(x) decreasing?
A. g(x) is flat for −1 ≤ x ≤ 0, and decreasing for 0 ≤ x ≤ 2
B. g(x) is not flat on any interval, but decreasing for 1 ≤ x ≤ 3
C. g(x) is flat for −1 ≤ x ≤ 0, and decreasing for 1 ≤ x ≤ 3
D. g(x) is not flat on any interval, but decreasing for 0 ≤ x ≤ 2
E. none of the above
Clicker Question 2
Head over heels
Suppose that g(x) is defined by
Z
g(x) =
8
f (t) dt
x
(with the variable on the bottom rather than the top). What is
g0 (x) then?
A. g0 (x) = −f (x)
B. g0 (x) = −f (8)
C. g0 (x) = f (x)
D. g0 (x) = f (8)
E. none of the above
One of the properties of
integrals tells us that
Z x
g(x) = −
f (t) dt.
8
Clicker Question 3
Composition of functions
Define h(x) = x3 and
Z
x
g(x) =
5
√
t+2
dt.
−1
What is the composition (g ◦ h)(x) = g(h(x))?
Z
x
A.
√
5
t+2
3
dt
−1
Z
x
√
B.
5
t+2
3
dt
−1
Z
x3
C.
√
5
Z−1
x √
D.
5
t+2
dt
t3 +2
dt
−1
E. none of the above