Fundamental limit asymptote help.

[renegade05]

Hello,

I have these problems:
Use limits to find:
Vertical asymptotes of: \(\displaystyle f(x)=\frac{sin(7-x)}{x^2-5x-14}\)
Horizontal asymptotes of: \(\displaystyle g(x)=\frac{2}{7+6e^{-3x}}\)

I need some help with the fundamentals of problems like this.

What do i plug in to find these limits? i graphed the first one and i can clearly see the va is x=-2 and i can kinda see how to get it. But if someone can show me how to do these problems the correct analytical way i would much appreciate that. need some starting pointers and help.

Thanks for the help as always!

 

[Deleted member 4993]

Hello,

I have these problems:
Use limits to find:
Vertical asymptotes of: \(\displaystyle f(x)=\frac{sin(7-x)}{x^2-5x-14}\)

You know that the vertical assymptote exist where the function becomes "undefined". That generally would be the roots of the denominator.

Most of the problem require different method. In this problem, you need to first factorize the denominator and observe that the limit actually exist for one of the roots.


Horizontal asymptotes of: \(\displaystyle g(x)=\frac{2}{7+6e^{-3x}}\)

what is the condition for horizontal assymptote?

I need some help with the fundamentals of problems like this.

Most of the problem require different method. In this problem, you need to first factorize the denominator

What do i plug in to find these limits? i graphed the first one and i can clearly see the va is x=-2 and i can kinda see how to get it. But if someone can show me how to do these problems the correct analytical way i would much appreciate that. need some starting pointers and help.

Thanks for the help as always!

 

[renegade05]

Hello,

I have these problems:
Use limits to find:
Vertical asymptotes of: \(\displaystyle f(x)=\frac{sin(7-x)}{x^2-5x-14}\)

You know that the vertical assymptote exist where the function becomes "undefined". That generally would be the roots of the denominator.

Most of the problem require different method. In this problem, you need to first factorize the denominator and observe that the limit actually exist for one of the roots.

Yes, i know that. But i dont know the correct notation/how to show it using limits. like what should i enter for the "lim x-> ???"

Horizontal asymptotes of: \(\displaystyle g(x)=\frac{2}{7+6e^{-3x}}\)

what is the condition for horizontal assymptote?

When x approaches infinity and neg infinity? What g(x) is approaching ?

I need some help with the fundamentals of problems like this.

Most of the problem require different method. In this problem, you need to first factorize the denominator

What do i plug in to find these limits? i graphed the first one and i can clearly see the va is x=-2 and i can kinda see how to get it. But if someone can show me how to do these problems the correct analytical way i would much appreciate that. need some starting pointers and help.

Thanks for the help as always!

 

[Deleted member 4993]

Hello,

I have these problems:
Use limits to find:
Vertical asymptotes of: \(\displaystyle f(x)=\frac{sin(7-x)}{x^2-5x-14}\)

You know that the vertical assymptote exist where the function becomes "undefined". That generally would be the roots of the denominator.

Most of the problem require different method. In this problem, you need to first factorize the denominator and observe that the limit actually exist for one of the roots.

Yes, i know that. But i dont know the correct notation/how to show it using limits. like what should i enter for the "lim x-> ???"

The vertical assymptotes would be at:

\(\displaystyle Lim_{x\to x_i}\)

where x[sub:gs5y2sss]i[/sub:gs5y2sss] are the roots of denominator.


Horizontal asymptotes of: \(\displaystyle g(x)=\frac{2}{7+6e^{-3x}}\)

what is the condition for horizontal assymptote?

When x approaches infinity and neg infinity? What g(x) is approaching ? Correct continue with the limit now
I need some help with the fundamentals of problems like this.

Most of the problem require different method. In this problem, you need to first factorize the denominator

What do i plug in to find these limits? i graphed the first one and i can clearly see the va is x=-2 and i can kinda see how to get it. But if someone can show me how to do these problems the correct analytical way i would much appreciate that. need some starting pointers and help.

Thanks for the help as always!