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

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August 23rd 2012, 02:28 PM
skinsdomination09

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)/tan² 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 tan² 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
August 23rd 2012, 02:37 PM
Plato

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)/tan² 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 $x=\frac{\pi}{2}$ on the left hand side.
August 23rd 2012, 02:44 PM
skinsdomination09

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
August 23rd 2012, 02:56 PM
Plato

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, $\tan \left( {\frac{\pi }{2}} \right) \ne 0~!$ .
August 23rd 2012, 03:14 PM
skinsdomination09

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, $\tan \left( {\frac{\pi }{2}} \right) \ne 0~!$ .

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?
August 23rd 2012, 05:26 PM
skeeter

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

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

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

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