Answer:
Yes, it is. Functions can only have one output (y) for each input (x). Furthermore, this means each x value will only have one y passing through it. Thus if we plot it on a graph and it passes through a horizontal line more than once, it is not a function. This is called the vertical line test.
(a)
![f'(x) = \frac{d}{dx}[\frac{lnx}{x}]](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Cfrac%7Blnx%7D%7Bx%7D%5D)
Using the quotient rule:
For maximum, f'(x) = 0;
(b) <em>Deduce:
</em>
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
, since ln(e) is simply equal to 1
Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
, as required.
Answer:
Hence, 5.64 centimeters of more rain fell in Dubaku's town than in Elliot's town.
Step-by-step explanation:
The amount of rain that fell in Dubaku's hometown is: 8 centimeters.
Amount of rain that fell in Elliot's hometown is: 2.36 centimeters.
We are asked to find how much more rain fell in Dubaku's town than in Elliot's town so it is calculated as the difference between the rain in both of there towns and is given by:
Difference in rain= 8-2.36
Difference in rain= 5.64 centimeters.
Answer:
January through
March
Step-by-step explanation:
