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:
Shrink:
a=1/4
a=0.3
Stretch:
a=60
a=2.5
a=1.1
Step-by-step explanation:
Answer:
4 inches.
Step-by-step explanation:
24 32
---- = -----
3 x
Cross multiply.
24x = (32)(3) = 96.
96 / 24 = 4.
Hope this helped and good luck! (:
In this number 1500,000,
1 is at million place and 5 is at hundred thousand place
So, the value of 1 = 1 (1,000,000) = 1 million
And the value of 5 = 5 (100,000 ) = 500,000 = Five hundred thousand
In the second number 100,500
1 is at hundred thousand place and 5 is at hundred place
The value of 1 = 1 (100,000) = 100,000 = Hundred thousand
And the value of 5 = 5 (100 ) = 500 = Five hundred
Since the digits 1 and 5 both are at different places in both the numbers so 1,500,000 and 100,500 are not the same.
Answer:
B. Angle 2 = Angle 3
Step-by-step explanation:
