Let ${s_n}_{n\in\Bbb N}$ be a sequence that converges to $L$ . This means for any $\varepsilon>0$ , there is some $N$ such that $|s_n-L|$ for all $n>N$ . From this inequality we see that $|(s_n-L)-0|$ , so it follows that $s_n-L\to0$ .

On the other hand, let ${s_n-L}$ be a sequence that converges to 0. This means $|(s_n-L)-0|$ for all large enough $n$ , and we get the simpler inequality for free, $|s_n-L|$ , so it follows that $s_n\to L$ .

3 0

2 years ago

When number can each term of the equation be multiplied by to eliminate the fractions before solving 6-3/4x+1/3=1/2x+5

PolarNik [594]

Answer:

Step-by-step explanation:

You need to find the least common denominator (LCD) to all the denominators of the fractions present in the equation. These denominators are (writing them in their prime factor form to make our calculations easier):

$4=2^2\\3=3\\2=2$

Therefore, we need to include a factor of 3, and two factors of 2 ( $2^2$ ) in our least common denominator, so this LCD will be a perfectly divided by all three given denominators, therefore eliminating all fractions in the equation.

Our LCD is = $3*2^2=13*4=12$

6 0

3 years ago

Fix the inequality below to correctly show the domain of<br> the function.

Nataliya [291]

Answer:

from questions it is given that X is lies between the -9 and -5. In this question X lies only between -9 to -5 but -9 and -5 are excluded because there is no equal sign given in the question. so value of X are (-8,-7,-6). and plot in the graph .and these values are the component of X so they are also a domain.

6 0

2 years ago