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.
Answer:
B) x - 4
Step-by-step explanation:
In this question, you have to simplify the expression to get your answer.
Solve:
1/2(2x - 8)
Use the distributive property.
1/2(2x) + 1/2(-8)
x + 1/2(-8)
x - 4
Your answer would be B) x - 4
Answer:
The 5 rational are 91/150 , 92/150 , 93/150 , 94/150 , 95/150
Step-by-step explanation:
We have to fine 5 rational numbers between
3/5 and 2/3
First we have to make the denominator same
3/5= 3/5 ×3/3 = 9/15 =9/15×10/10 =90/150
2/3 = 2/3×5/5 = 10/15 = 10/15×10/10 = 100/150
The 5 rational numbers are
91/150 , 92/150 , 93/150 , 94/150 , 95/150
hope this helps :)
