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Allushta [10]
3 years ago
9

Identify the horizontal asymptote of f(x) = quantity 2 x minus 1 over quantity x squared minus 7 x plus 3.

Mathematics
1 answer:
Rina8888 [55]3 years ago
3 0
We must recall that a horizontal asymptote is the value/s of y that the given function approaches to but never reaches. To find this in a rational function, we compare the expressions with highest degree in the numerator and denominator. There are three possible outcome when this happens.

1. if the highest degree (highest exponent) in the numerator is bigger than that of the denominator, then there won't be any horizontal asymptote.

2. if the highest degree in the denominator is bigger, then the horizontal symptote would be y = 0.

3. if they have the same highest degree, then we just get the quotient of their coefficient. 

Now, going back to our function, we have

f(x) = \frac{2x - 1}{x^{2} - 7x + 3}

From this we can see that the highest degree in the numerator is 1 (from 2x) and 2 (from x²) for the denominator. Clearly, it shows that its denominator has a higher degree. And from our discussion, we can conclude that the horizontal asymptote would be y = 0.

Answer: y = 0
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ANSWER

C) 1, 3, 6, 10, 15, 21, 28, 36, 45

EXPLANATION

The recursive formula is,

t_1=1,t_n=t_{n-1}+n

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When n=2,

t_2=t_{2-1}+2

t_2=t_{1}+2 = 1 + 2 = 3

when n=3,

t_3=t_{2}+2 = 3 + 3= 6

when t=4,

t_4=t_{3}+2 = 6+ 4= 10

When t=5,

t_5=t_{4}+5 = 10 + 5 = 15

when t=6,.

t_6=t_{5}+6 = 15 + 6 = 21

when t=7

t_7=t_{6}+7 = 21 + 7 = 28

When t=8,

t_8=t_{7}+8 = 28 + 8 = 36

When t=9,

t_9=t_{8}+9 = 36 + 9 = 45

Hence the first nine triangular number are

C) 1, 3, 6, 10, 15, 21, 28, 36, 45

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The proportions of an item must always add up to one. This means that if you added the 1/3 to the 2/5 and then to the fraction Charlie watch at night, they should add up to one.

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