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Paraphin [41]
3 years ago
14

Let f(x)=20/1+9e^3x .

Mathematics
2 answers:
Alex777 [14]3 years ago
6 0
The answer is the last one
butalik [34]3 years ago
5 0

Answer:

y = 0 and y = 20

Step-by-step explanation:

The given function is \left(\frac{20}{\left(1+9e^{3x}\right)}\right)

There is no vertical asymptotes because the denominator will never be zero.

Horizontal asymptotes are given by

y=\lim _{x\to -\infty }f(x)\\\\y=\lim _{x\to \:-\infty \:}\left(\frac{20}{1+9e^{3x}}\right)

Take the constant 20 out of the limit

20\cdot \lim \:_{x\to \:-\infty \:}\left(\frac{1}{1+9e^{3x}}\right)

Now, we can further simplify as follows

y=20\cdot \frac{\lim _{x\to \:-\infty \:}\left(1\right)}{\lim _{x\to \:-\infty \:}\left(1+9e^{3x}\right)}\\\\y=20\cdot \frac{1}{1}\\\\y=20

Similarly, the second horizontal asymptote is

y=\lim _{x\to \infty }\left(\frac{20}{\left(1+9e^{3x}\right)}\right)

We can simplify this limit as we did the previous one

y=20\cdot \frac{\lim _{x\to \infty \:}\left(1\right)}{\lim _{x\to \infty \:}\left(1+9e^{3x}\right)}\\\\y=20\cdot \frac{1}{\infty \:}\\\\y=0

Hence, asymptotes of the graph of f(x) are

y = 0 and y = 20

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<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.

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