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:
1) 257
2) 24^1=24
3) 47/8(Decimal: 5.875) How to: 5/1+7/8 = 40/80+7/8 = 40 + 7 / 8 <em>=</em><em> </em><em>4</em><em>7</em><em>/</em><em>8</em>
4)=920
5) =32.484
6) =33.444
7) = 4 : 1 How to: The GCF of 12 and 3 is 3 Divide both terms by the GCF, 3:
12 ÷ 3 = 4
3 ÷ 3 = 1 The ratio 12 : 3 can be reduced to lowest terms by dividing both terms by the GCF = 3 :
12 : 3 = 4 : 1
8) = 9 cups. How to: 2*3=6. so you multiply the other side (3) by 3 so 3*3=9 cups.
9) The second pack weighs more. How to: Since 45 ounces is 2.812 pounds (Formula
divide the mass value by 16) and 2.812 is less than 3 so second pack weighs more.
10) =26.6
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Answer:
rational
Step-by-step explanation:
because it not a repeating decimal that never ends without repeating number and can be writing in as form of fraction. 23+777=800 definitely rational
Answer:
10.50 is the interest
Step-by-step explanation:
B = p(1 + r)^t
P = 50
r = .10
t = 2
B = 50(1 + .1)^2
= 50(1.1)^2
= 50(1.21)
= 60.5
But we want to know the interest and this is the balance
60.5- 50 = 10.5
Sum of two negatives is a positive
