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 .
Hello from MrBillDoesMath!
Answer:
.08%
Discussion:
Let the percent be denoted "p". Then
2000 * p% = 160 => ( as p% = p/100)
2000* p/100 = 160 =>
20p = 160 =>
p = 8 or .08%
Regards,
MrB
Answer:
7x+54
Step-by-step explanation:
because you distribute the 7 to the x and the 8 first then you bring that down which becomes 7x+56 then you to the addition so you do 56+-2 which would give you 54.
The graph looks like this, on the enclosed pic:
One feature is that it's periodic and torn (has cut-off points), meaning the domain is the same as in case of tan(x): x€R and x =/= π/2+πn.
The range equals the range of arcsin(x): -π/2<=y<=π/2 OR y€[-π/2;π/2]
Hope could understand and if it helped! :)
Answer:
Option 1
Figure Length (feet) Width (feet)
small rectangle 14 6
large rectangle 20 7
Figure Base (feet) Height (feet)
triangle 6 6
Option 2
Figure Length (feet) Width (feet)
small rectangle 6 7
large rectangle 14 13
Figure Base (feet) Height (feet)
triangle 6 6
Step-by-step explanation:
