So i need to pick classes for my freshman year next year and i d k if i should take pre algebra or just do algebra. My math grad
1 answer:
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By definition of absolute value, you have
or more simply,
On their own, each piece is differentiable over their respective domains, except at the point where they split off.
For <em>x</em> > -1, we have
(<em>x</em> + 1)<em>'</em> = 1
while for <em>x</em> < -1,
(-<em>x</em> - 1)<em>'</em> = -1
More concisely,
Note the strict inequalities in the definition of <em>f '(x)</em>.
In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:
All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.
Answer:
Present value = $4,122.4
Accumulated amount = $4,742
Step-by-step explanation:
Data provided in the question:
Amount at the Start of money flow = $1,000
Increase in amount is exponentially at the rate of 5% per year
Time = 4 years
Interest rate = 3.5% compounded continuously
Now,
Accumulated Value of the money flow =
The present value of the money flow =
=
=
=
= 1000 × [70.7891 - 66.6667]
= $4,122.4
Accumulated interest =
=
= $4,742