So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
2X +2(15)=46
What is X?
2X+30=46
-30 -30
________
2X=16
X=8
<span>2153.28 hundreds to be exact or, 2153.</span>
Answer:
x = 25
Step-by-step explanation:
Given:
Amount invest p = Tk.x
Number of year t = 4
Rate r = x%
Profit = Tk.x
Find:
Value of x
Computation:
Profit = prt / 100
Tk.x = [(Tk.x)(x)(4)] / 100
x = 100 / 4
x = 25
Answer:
Having public authority in society is there to protect our rights, such as life liberty, and property. They are there to help keep things safe. Public authority is not to demand obedience from citizens it is there to protect them from any harm.
Step-by-step explanation:
