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
if satisfied with the
explanation, please rate it up..
milcah answered 2 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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For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
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Consider a continuous random variable X with the probability
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Consider Y = g( X ) = 100/(x^2+1). Use cdf approach to find the cdf
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=
Prove that if f, g are integrable, then the function (f(x) + cos(x)g(x))2is integrable.
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1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c)...
1) Let f(x) be a continuous, everywhere differentiable function
and g(x) be its derivative. If f(c) = n and g(c) = d, write the
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x, c, n, and d. You may use point-slope or slope-intercept but do
not introduce more variables.
2) Let f(x) be a continuous, everywhere differentiable function.
What kind information does f'(x) provide regarding f(x)?
3) Let f(x) be a continuous, everywhere differentiable...
Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f...
Let f be a continuous function on [a, b] which is differentiable
on (a,b). Then f is non-decreasing on [a,b] if and only if f′(x) ≥
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can you please prove this theorem? thank you!
True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x|...
True and False (No need to solve).
1. Every bounded continuous function is
integrable.
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
continuous function.
4. Bisection algorithm is based on the fact that If f is a
continuous function and f(x1) and f(x2) have
opposite signs, then the function f has a root in the interval
(x1,...
2 Consider the probability density function (p.d.f) of a continuous random variable X: f(x) = (...
2 Consider the probability density function (p.d.f) of a
continuous random variable X: f(x) = ( k x3 , 0 < x < 1, 0,
elsewhere, where k is a constant. (a) Find k. (b) Compute the
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X < 0.8). (d) Compute µX = E(X) and σX.
f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...
f is a twice differentiable function and that its
second partial derivatives are continuous.
Let h(t) =
f (x(t), y(t)) where
x = 2e t and y =
t.
Suppose that fx(2, 0) = 3,
fy(2, 0) = 2,
fxx(2, 0) = 4,
fyy(2, 0) = 3, and
fxy(2, 0) = 1.
h'(t) = fx * 2e t+
fy
find h''(t) when t = 0.
(I don't understand how for the second partial derivative d/dy
(fy) = d/dt (x) *fyx...
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