Answer:
1st term= 8 2nd term=6 3rd term=4 4th term=2 5th term=0 6th term=-2 7th term=-4 8th term=-6 9th term=-8 10th term=-10
Step-by-step explanation:
hope this helps
Answer:
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![f(15) = 62826](https://tex.z-dn.net/?f=f%2815%29%20%3D%2062826)
Step-by-step explanation:
Given
In 1990; Income= $39000
In 2010; Income= $70768
Solving (a): An equation in form of f(x) = ax + b
First, we need to determine the slope, a
![a = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Taking y as income and x as year index.
When x = 0; y = 39000
When x = 20; y = 70768
Substitute these values in the above formula
![a = \frac{70768 - 39000}{20 - 0}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B70768%20-%2039000%7D%7B20%20-%200%7D)
![a = \frac{31768}{20}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B31768%7D%7B20%7D)
![a = 1588.4](https://tex.z-dn.net/?f=a%20%3D%201588.4)
Next, is to determine the formula using:
![y - y_1 = a(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20a%28x%20-%20x_1%29)
<em>Considering :When x = 0; y = 39000, we have</em>
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<em>Make y the subject of formula</em>
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<em>Express y as a function of x</em>
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Solving (b): Income in 2005
<em>In 2005, x = 15</em>
So:
becomes
![f(15) = 1588.4 * 15 + 39000](https://tex.z-dn.net/?f=f%2815%29%20%3D%201588.4%20%2A%2015%20%2B%2039000)
![f(15) = 62826](https://tex.z-dn.net/?f=f%2815%29%20%3D%2062826)
Answer:
3
Step-by-step explanation:
lim(t→∞) [t ln(1 + 3/t) ]
If we evaluate the limit, we get:
∞ ln(1 + 3/∞)
∞ ln(1 + 0)
∞ 0
This is undetermined. To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.
lim(t→∞) [t ln(1 + 3/t) ]
lim(t→∞) [ln(1 + 3/t) / (1/t)]
This evaluates to 0/0. We can simplify a little with u substitution:
lim(u→0) [ln(1 + 3u) / u]
Applying L'Hopital's rule:
lim(u→0) [1/(1 + 3u) × 3 / 1]
lim(u→0) [3 / (1 + 3u)]
3 / (1 + 0)
3
Answeep-by-step explanation:
he was 76
jk i am stupid and this is nit the right i just wanted to know how t felt to help someone