F f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?
1 answer:
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Differentiating the function
... g(x) = 5^(1+x)
we get
... g'(x) = ln(5)·5^(1+x)
Then the linear approximation near x=0 is
... y = g'(0)(x - 0) + g(0)
... y = 5·ln(5)·x + 5
With numbers filled in, this is
... y ≈ 8.047x + 5 . . . . . linear approximation to g(x)
Using this to find approximate values for 5^0.95 and 5^1.1, we can fill in x=-0.05 and x=0.1 to get
... 5^0.95 ≈ 8.047·(-0.05) +5 ≈ 4.598 . . . . approximation to 5^0.95
... 5^1.1 ≈ 8.047·0.1 +5 ≈ 5.805 . . . . approximation to 5^1.1
2) 200 mL
3) 0.2 kg
Step-by-step explanation:
2)
In this problem, we know that:
- With 1 liter of juice, we can fill a total of 5 cups
So we know that the total volume of 5 cups is equal to
V = 1 L
This means that the volume of each cup is equal to the total volume divided by the number of cups (5), therefore:
And keeping in mind the equivalence between liters and milliliters:
1 L = 1000 mL
This means that the capacity of each cup is
3)
Here we want to find the mass contained in each cup.
We know that the mass of a substance is related to each volume by the equation
where
d is the density
m is the mass
V is the volume
In this problem, we have:
V = 0.2 L is the volume of juice in each cup
is the density of juice (assuming it is the same as the density of water)
So, the mass of juice in one cup is: