Limits Help please (l'hospital's rule and such)

Sorry, I'm sure the questions i'm about to ask are simple to all of you out there but I really haven't had an easy time with Calc.

**what is the limit as x approaches pi/2 from the left of**

(tan x + 3)/tanē x

So I don't get it, when doing limits from the left and right are the procedures the same? Substitute in the limit, and if that becomes indetirminate use l'hospitals rule?

tan (pi/2) +3 would give me 3 and tanē x would give me 0. So i'd have 3/0 and thus this would be undefined and not indetirminate?

I'm really not confident in my answer and I would like to get this stuff down!!

Please help and thank you so much to every person who takes the time to assist me.

**This is a no calculator question**

Re: Limits Help please (l'hospital's rule and such)

Quote:

Originally Posted by

**skinsdomination09** Sorry, I'm sure the questions i'm about to ask are simple to all of you out there but I really haven't had an easy time with Calc.

**what is the limit as x approaches pi/2 from the left of**

(tan x + 3)/tanē x

So I don't get it, when doing limits from the left and right are the procedures the same? Substitute in the limit, and if that becomes indetirminate use l'hospitals rule?

Limits are a very *visual* topic in calculus.

**Draw a graph.** Then look at the graph at $\displaystyle x=\frac{\pi}{2}$ on the left hand side.

Re: Limits Help please (l'hospital's rule and such)

with all due respect how am I supposed to know the graph of (tan x + 3)/ tan squared x?

this is a non calculator question.

I'm aware that I can do them visually but that's a little over the top

Re: Limits Help please (l'hospital's rule and such)

Quote:

Originally Posted by

**skinsdomination09** with all due respect how am I supposed to know the graph of (tan x + 3)/ tan squared x?

this is a non calculator question.

I'm aware that I can do them visually but that's a little over the top

Why did you not say that? Do you expect mind-readers here?

**You need to learn some basic trigonometry**, $\displaystyle \tan \left( {\frac{\pi }{2}} \right) \ne 0~!$.

Re: Limits Help please (l'hospital's rule and such)

Quote:

Originally Posted by

**Plato** Why did you not say that? Do you expect mind-readers here?

**You need to learn some basic trigonometry**, $\displaystyle \tan \left( {\frac{\pi }{2}} \right) \ne 0~!$.

yeah sorry, I definetely overlooked that.

you're right, I was thinking 1/0 = 0. So it'd signal a V. as. which would mean either pos/neg infinity?

so i'd pick a near by point to tell which one it would be, lets say 2pi/3 which would give me neg. radical three and since 1 rad = 0 it is getting more negative towards 90 degrees so from the left it would be approaching **negative** infinity?

is that correct?

Re: Limits Help please (l'hospital's rule and such)

$\displaystyle \frac{\tan{x}+3}{\tan^2{x}} = \frac{1}{\tan{x}} + \frac{3}{\tan^2{x}}$

as $\displaystyle x \to \frac{\pi}{2}^+$ , $\displaystyle \tan{x} \to +\infty$ ...

now, what happens to the sum of the last two fractions above?