Answer:
Step-by-step explanation:
The Fundamental Theorem of Calculus states that:
![\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20%5Cint_a%5Ex%20f%28t%29%5C%2C%20dt%20%20%5Cright%5D%20%3D%20f%28x%29)
Where <em>a</em> is some constant.
We can let:
By substitution:
Taking the derivative of both sides results in:
![\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%27%28s%29%20%3D%20%5Cfrac%7Bd%7D%7Bds%7D%5Cleft%5B%20%5Cint_6%5Es%20g%28t%29%5C%2C%20dt%5Cright%5D)
Hence, by the Fundamental Theorem:
Answer: T = 4c + 4t + 3s
Step-by-step explanation:
Stocks contains:
4-legged chairs
4-legged tables
3-legged stools
So, 1 chair has legs = 4
So, c chairs has legs = 4c
1 table has legs = 4
So, t tables has legs = 4t
1 stool has legs = 3
So, s stools has legs = 3s
Let T denotes the total no. of legs
So, the total number of furniture legs in aisle 2 :
T = 4c + 4t + 3s
Answer:
f(-3)= - (-3)+5= +3 +5 = 8
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
