In: Math
Consider a continuous, integrable, twice-differentiable function
f with input variable x.
In terms of the units of f and the units of x, choose the units of
each function or expression below:
(a) The units of f ' are
the units of
f
the units of
x
(the units of f)(the units of x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(b) The units of f '' are
the units of
f
the units of
x
(the units of f)(the units of x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(c) The units of
b | f(x)dx |
a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(d) The units of
b | f '(x)dx |
a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(e) The units of
n | f(xi)Δx |
i=1 |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(f) The units of
f(b)−f(a) |
b−a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(g) The units of
d |
dx |
x | f(t)dt |
a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(h) The units of
d2 |
dx2 |
x | f(t)dt |
a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |
(i) The units of h in
f(a+h)−f(a) |
h |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
the units of f |
the units of x |
the units of f |
(the units of x)2 |
the units of f |
(the units of x)3 |