The choices are the same for both.

Mathematics

2 answers:

densk [106]3 years ago

5 0

Answer:

f(-∞) -∞

f(∞) = -∞

Step-by-step explanation:

f(x) = -8x^4 +3x^2 -7x

-----------------------

4x^2 -4

The -8x^4 / 4x^2 will dominate at infinity

f(x) can be approximated at ±∞ by -2 x^2

f(-∞) = -2(-∞)^2 = -2 *∞ = -∞

f(∞) = -2(∞)^2 = -2 *∞ = -∞

dlinn [17]3 years ago

3 0

Answer:

- $\infty$

Step-by-step explanation:

f(x)=\frac{-8x^4+3x^2-7x}{4x^2-4}=\frac{-8x^2+3-7/x}{4-4/x^2}

As x approaches -\infty, f(x) will tend to -\infty

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A fruit fly experiment starts with 600 flies. If the number of flies after x days is given by the function P(x)=600e^0.3x, how m

slega [8]

Since ln(x) is the inverse of e^x and we want to find out when P(x)=1000, we will substitute P(x) by 1000 and then solve for x days.

1600e^0.3x = 1000

Divide 600 for both sides you will get:

5/3 = e^0.3x

Multiply ( ln ) for both sides and then divide by 0.3.

(ln 5/3)/(0.3) = x

x = 1.7

So there will be 1000 flies in approximately 1.7 days

6 0

3 years ago

Answer the question with explanation;

PSYCHO15rus [73]

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

$\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0$

Therefore, by the series divergence test, the series $\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}$ diverges.

EDIT: To VectorFundament120, if $(x_n)_{n\in\mathbb N}$ is a sequence, both $\lim x_n$ and $\lim_{n\to\infty}x_n$ are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.