Answer:
- The instantaneous rate of increase of f(x) at
is 3. - One possible equation of this line is y = 3x - 16.
- The line is tangent to the graph of y = f(x). The slope of the line is the same as the instantaneous rate of increase of f(x) at .
Step-by-step explanation:
<h3>1.</h3>
![\begin{aligned}&\lim_{h\to 0}{\frac{f(3+h)-f(h)}{h}}\\ =&\lim_{h\to 0}\frac{1}{h} \cdot [(3^{3} + 3 \times 3^{2}h +3\times 3h^{2} + h^{3})- 4(3^{2} + 2\times 3h + h^{2}) + 2 \\[-1em] &\phantom{\lim_{h\to 0}\frac{1}{h}\cdot []} -(3^{3} -4\times 3^{2} + 2)]\\ = &\lim_{h \to 0}\frac{h^{3} + 5h^{2} +3h}{h}\\=& \lim_{h \to 0}{h^{2}} + \lim_{h \to 0}{5h} + \lim_{h\to 0}{3}\\ =& 3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Clim_%7Bh%5Cto%200%7D%7B%5Cfrac%7Bf%283%2Bh%29-f%28h%29%7D%7Bh%7D%7D%5C%5C%20%3D%26%5Clim_%7Bh%5Cto%200%7D%5Cfrac%7B1%7D%7Bh%7D%20%5Ccdot%20%5B%283%5E%7B3%7D%20%2B%203%20%5Ctimes%203%5E%7B2%7Dh%20%2B3%5Ctimes%203h%5E%7B2%7D%20%2B%20h%5E%7B3%7D%29-%204%283%5E%7B2%7D%20%2B%202%5Ctimes%203h%20%2B%20h%5E%7B2%7D%29%20%2B%202%20%5C%5C%5B-1em%5D%20%26%5Cphantom%7B%5Clim_%7Bh%5Cto%200%7D%5Cfrac%7B1%7D%7Bh%7D%5Ccdot%20%5B%5D%7D%20-%283%5E%7B3%7D%20-4%5Ctimes%203%5E%7B2%7D%20%2B%202%29%5D%5C%5C%20%3D%20%26%5Clim_%7Bh%20%5Cto%200%7D%5Cfrac%7Bh%5E%7B3%7D%20%2B%205h%5E%7B2%7D%20%2B3h%7D%7Bh%7D%5C%5C%3D%26%20%5Clim_%7Bh%20%5Cto%200%7D%7Bh%5E%7B2%7D%7D%20%2B%20%5Clim_%7Bh%20%5Cto%200%7D%7B5h%7D%20%2B%20%5Clim_%7Bh%5Cto%200%7D%7B3%7D%5C%5C%20%3D%26%203%5Cend%7Baligned%7D)
.
<h3>2.</h3>
.
In other words, the graph of y = f(x) passes through the point (3, -7) where 
.
The point-slope form of a line in a cartesian plane is:
.
For this line,
is the point on the line, while
is the slope of the line.
The equation of this line will thus be
.
That's equivalent to
.
<h3>3.</h3>
Refer to the diagram attached. The line touches the graph of y = f(x) at x = 3 without crossing it. The line here is thus a tangent to the graph of y = f(x) at x = 3. The slope of the line represents the instantaneous rate of increase of f(x) at .
Answer:
<h2>Addition Property of Equality</h2>
Step-by-step explanation:
When doing algebra, you need to reverse operations. When you reverse an operation, you use one of the properties. For example, if you add 3x to undo subtracting 3x, you are using the addition property of equality, because the equation still equal.
<h2>I'm always happy to help :)</h2>
Answer:
10.30721
Step-by-step explanation:
This requires conversion, this is Liters to Gallons.
1 LITER= 0.26417205
so knowing this info. we just plug in
39 L = 10.30721 gallons
Hope this helped! :)
Answer:
$0.69 for each bag
Step-by-step explanation:
Since you have 12 bags for $8.25, that means you need to divide the price by the number of bags to get the price of each:
You then need to round to the nearest hundredths. Since the number after the hundredths place is a 7, which is greater than or equal to 5, you need to add 1 to the hundredths place making the final answer $0.69
So:
(x-4)(x+2) / (x-4)(x+4)
We cancel out the x - 4:
(x+2)/(x+4)
Restrictions: x ≠ 4, x ≠ -4
