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Aneli [31]
3 years ago
10

Can you please help me ​

Mathematics
1 answer:
Dmitrij [34]3 years ago
4 0

Answer:

ok I can. what is the question?

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Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i
jenyasd209 [6]

Answer:

If the limit that you want to find is \lim_{x\to \infty}\dfrac{P(x)}{Q(x)} then you can use the following proof.

Step-by-step explanation:

Let P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} and Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0} be the given polinomials. Then

\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}

Observe that

\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}

and

\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}

Then

\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}

3 0
3 years ago
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!! The equal sections of a spinner have one of the following letters: A, B, A, C, B. Predict
Eddi Din [679]

Answer:

the 3rd A

Step-by-step explanation:

ABACB = 5 altogether

ABACB ABA = 8

5 0
3 years ago
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each day last week, Ms. wilson walked3/4 mile. what is the total distance, in miles, that Ms. Wilson walked in 4 days?
zloy xaker [14]
Hey there! :D

Since she walks 3/4 a mile a day, we can multiply that by 4.

3/4= .75

4*.75= 3

She walked 3 miles in 4 days.

I hope this helps!
~kaikers
6 0
3 years ago
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You make a dessert with lemon gelatin and lime gelatin. What percent of the dessert is lime-flavored? Explain
pentagon [3]

Answer:

i struggle with this to sry and hey

Step-by-step explanation:

8 0
2 years ago
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15% of people on the beach do not wear sun screen. If 30 people don't wear sunscreen, what is the total number of people at the
lara [203]

Answer: The information you are given shows that 15% = 30. Multiply 30 by 6 and 2/3 (The number of times 15 goes into 100) and you have your answer. There are 200 people on the beach.

6 0
3 years ago
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