Question

Complete the table for the function and find the indicated limit.

Answer 1

\[\lim_{x \rightarrow 0} \frac{ x^2 }{ \sin x }\]

Answer 2

https://study.ashworthcollege.edu/access/content/group/0eb36323-b565-4bd6-bb22-afe8d36d4e8a/Precalculus_Exam_11/images/f1q14g3.jpg

Answer 3

A. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = -1

B. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0

C. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0.1

D. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 1

Answer 4

Would the answer be B? Isn't it discontinuous?

Answer 5

im sorry I have no idea :(

Answer 6

so, what values did you get for the table?

Answer 7

they should match one of the choices I'd think

Answer 8

How would you begin this problem? Would you first substitute for 0?

Answer 9

well, you simply finish up the table :)

Answer 10

you have an "x" atop, just get the f(x)

Answer 11

And how do you find the limit exactly? I'm sorry, I'm just really bad at this.

Answer 12

well, what values did you get?

Answer 13

the limit is just where f(x) is moving towards

Answer 14

lemme give you a quick table so you can see
say
$$
\begin{matrix}
x&&y \\
hline\\
2.3&& 6\\
2.4&& 7\\
2.5&& 8\\
2.8&& 9\\
\color{blue}{3}&& \color{blue}{10}\\
3.7&& 14\\
3.6&& 13\\
3.5&& 12\\ \end{matrix}
$$

Answer 15

so, as you can see, as "x" is one value, f(x) or "y", takes on whatever value
as x -> 3 y goes to 10
or
as "x" goes to 3, the limit of "y" is 10

Answer 16

on the example above, "x" takes on values "before" and "after" 3
and notice how "y" is ever growing towards, or shrinking towards, 10

Answer 17

$$
\begin{matrix}
x&&y \\
\hline\\
2.3&& 6\\
2.4&& 7\\
2.5&& 8\\
2.8&& 9\\
\color{red}{3}&& \color{red}{10}\\
3.5&& 12\\
3.6&& 13\\
3.7&& 14\\
3.8&& 15
\end{matrix}
$$

Answer 18

like so

Answer 19

I kind of get it, I think. Well, your example at least

Answer 20

your exercise is exactly the same, just different values

Answer 21

so let's do the table
let's see, lemme fire up my calculator

Answer 22

I think it is B because the values are getting closer and closer to zero

Answer 23

so I get
-0.03000450047254484
-0.02000133339555818
-0.01000016666861113
0.01000016666861113
0.02000133339555818
0.03000450047254484

Answer 24

Yes I got those values

Answer 25

so the function looks like
so yes, is approaching 0

Answer 26

thus the liimit is 0

Answer 27

Thanks so much!

Answer 28

yw