Find the linear approximation of the function g(x) = 5 1 + x at a = 0. g(x) ≈ use it to approximate the numbers 5 0.95 and 5 1.1
. (round your answers to three decimal places.) 5 0.95 ≈ 5 1.1 ≈ illustrate by graphing g and the tangent line. webassign plot webassign plot webassign plot webassign plot
1 answer:
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
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Answer:
The theater has 32 rows
Step-by-step explanation:
The rule of the sum of n terms of an arithmetic sequence is S =
(a + l), where
- a is the first term
- l is the last term
- n is the number of the terms
∵ The number of seats per row follows an arithmetic sequence
∵ The first row has 26 seats
∴ a = 26
∵ The last row has 150 seats
∴ l = 150
∵ The theater seats are 2,816
∴ S = 2,816
→ Substitute these values in the rule of the sum above to find n
∵ 2,816 = (26 + 150)
∴ 2,816 = (176)
∴ 2,816 = 88n
→ Divide both sides by 88
∴ 32 = n
∵ n represents the number of the rows
∴ The theater has 32 rows
When you compare two functions f(x) and g(x), you're looking for a special input such that
Since you have the table with some possible candidates for , you simply have to choose the row that gives values for f(x) and g(x) that are as close as possible (the exact solution would give the same value for f(x) and g(x), so the approximate solution will give values for f(x) and g(x) that are close to each other).
In your table, the values for f(x) and g(x) are closer when x=-0.75
Answer:
x= 45
y= 18.5 (3 s.f.)
Step-by-step explanation:
Since the quadrilateral has 4 equal sides, it is a square and hence the 4 angles are right angles.
I have drawn the 2 triangles of the square separately for better understanding.
Please see the attached pictures for full solution.
