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

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