1 continuity and 2 limit laws problems

[namburger]

Thanks so much for the help

PROBLEM 1) Use continuity to evaluate the limit.

lim x→16​

20 + x

20 + x

OK this problem is hard at all, but I have no clue what webassign wants from me bro
Consider the intervals for which the numerator and the denominator are continuous.

The numerator 20 +

x

is continuous on the interval

The denominator

20 + x

is continuous and nonzero on the interval6





Problem 2:


Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim t→0​

3

t 1 + t

−

3

t

Problem 3:


Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim x→−24​

x2 + 49 − 25

x + 24

 

[stapel]

Your copy-n-paste from your online assessment is not displaying correctly, at least not for those of us who aren't able to access the online source for your material. (I'm guessing that your post has been left so confusing is because the contents are displaying differently for you.)

To learn how to type math as text, please review this article.

PROBLEM 1) Use continuity to evaluate the limit.

lim x→16​

20 + x

20 + x

I will guess that you mean something along the lines of the following:

. . . . .limit, x -> 16, (20 + sqrt[x]) / sqrt[20 + x]

...which typesets as:

. . . . .\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 16}\, \dfrac{20\, +\, \sqrt{\strut x\,}}{\sqrt{\strut 20\, +\, x\,}}\)

Please reply with confirmation or else corrections.

OK this problem is hard at all...

Do you mean that it "is not hard at all"...?

but I have no clue what webassign wants from me

We didn't write the software, nor did we set up your assignment. We can't know what the "back end" is expecting, either. Sorry.

Consider the intervals for which the numerator and the denominator are continuous.

The numerator 20 +

x

is continuous on the interval

I have no idea what you mean by the above...?

The denominator

20 + x

is continuous and nonzero on the interval6

I have no idea what you mean by "interval6". Sorry.

---

Problem 2: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim t→0​

3

t 1 + t

−

3

t

I think the above means the following:

. . . . .limit, t -> 0, { [ 3 / (t / sqrt[1 + t]) ] / [3 / t] }

...which typesets as:

. . . . .\(\displaystyle \displaystyle \lim_{t\, \rightarrow\, 0}\, \dfrac{ \left(\dfrac{3}{ \left(\dfrac{t}{\sqrt{\strut 1\, +\, t\,}}\right)}\right) }{ \left(\dfrac{3}{t}\right) }\)

(Sorry about the weird spacing....)

Is this correct? When you reply, please include a clear listing of your efforts so far.

---

Problem 3: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim x→−24​

x2 + 49 − 25

x + 24

I think the above means the following:

. . . . .limit, x -> -24, { sqrt{x^2 + 49} / (-25) } / {x + 24}

...which typesets as:

. . . . .\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, -24}\, \dfrac{ \left(\dfrac{\sqrt{\strut x^2\, +\, 49\,}}{-25}\right) }{x\, +\, 24}\)

Is this correct? When you reply, please include a clear listing of your efforts so far.

Thank you!