Determine the x- and y-intercepts of the graph of y=−12x−4 .

Mathematics

1 answer:

aleksley [76]3 years ago

3 0

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Determine whether the following series converge or diverge

Mars2501 [29]

An alternating series $\sum\limits_n(-1)^na_n$ converges if $|(-1)^na_n|=|a_n|$ is monotonic and $a_n\to0$ as $n\to\infty$ . Here $a_n=\dfrac1{\ln(n+1)}$ .

Let $f(x)=\ln(x+1)$ . Then $f'(x)=\dfrac1{x+1}$ , which is positive for all $x>-1$ , so $\ln(x+1)$ is monotonically increasing for $x>-1$ . This would mean $\dfrac1{\ln(x+1)}$ must be a monotonically decreasing sequence over the same interval, and so must $a_n$ .

Because $a_n$ is monotonically increasing, but will still always be positive, it follows that $a_n\to0$ as $n\to\infty$ .

So, $\sum\limits_n(-1)^na_n$ converges.

5 0

3 years ago

55% of what number is 231

babunello [35]

.55*X=231 .....X=231/.55.......X= 420

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3 years ago

When Pheobe asked her friends about their Thanksgiving, 35% of her 60 friends said they had pumpkin pie for dessert. How many fr

nataly862011 [7]

Answer:

Step-by-step explanation:

I dunno, I used a calculator B)