Question
In: Math
Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units...
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 |
Solutions
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milcah answered 3 years agoRelated Solutions
Suppose f is a twice differentiable function such that f′(x)>0 and f′′(x)<0 everywhere, and consider the...
Suppose f is a twice differentiable function such that
f′(x)>0 and f′′(x)<0 everywhere, and consider the following
data table.
x
0
1 2
f(x) 3
A B
For each part below, determine whether the given values of A and
B are possible (i.e., consistent with the information about f′and
f′′ given above) or impossible, and explain your answer.
a)A= 5, B= 6
(b)A= 5, B= 8
(c)A= 6, B= 6
(d)A= 6, B= 6.1
(e)A= 6, B= 9
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Let f be a continuous function on [a, b] which is differentiable
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can you please prove this theorem? thank you!
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True and False (No need to solve).
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2. f(x)=|x| is not integrable in [-1, 1] because the function f
is not differentiable at x=0.
3. You can always use a bisection algorithm to find a root of a
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