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

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    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
    Last edited by skinsdomination09; August 23rd 2012 at 02:44 PM.
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    Re: Limits Help please (l'hospital's rule and such)

    Quote Originally Posted by skinsdomination09 View Post
    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 x=\frac{\pi}{2} on the left hand side.
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    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
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    Re: Limits Help please (l'hospital's rule and such)

    Quote Originally Posted by skinsdomination09 View Post
    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~!.
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    Re: Limits Help please (l'hospital's rule and such)

    Quote Originally Posted by Plato View Post
    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?
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    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?
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