1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Does this limit exist lim e^(r^2)/(cos(t)sin(t)) for (r,t)->(0,0)

  1. Apr 12, 2005 #1
    In my exam the question was to determine the existence of this limit
    [tex] \lim_{(r,t)\rightarrow(0,0)} \frac{e^{r^2}}{\cos{t}\sin{t}} [/tex]

    now i wrote the numerator has no t associated with it so grows or shrinks without bounds, the same applies for the denominator...
    so the limit does not exist

    is this a good reason

    another question was
    [tex] \lim_{(x,y)\rightarrow(0,0)} \frac{\sin{xy}}{xy} [/tex]
    i substituted xy = u and got [tex] \lim_{u \rightarrow 0} \frac{\sin{u}}{u} = 1 [/tex]

    is this the correct method?
    Am i right?
  2. jcsd
  3. Apr 12, 2005 #2


    User Avatar
    Science Advisor

    The numerator does not "grow or shrink without bound". As r goes to 0, the numerator goes to 1.

    However, you are correct that the denominator goes to 0 as t does no matter what r is. Since the numerator goes to 1, what does that tell you about the fraction?

    I was a bit suspicious about your second method, but yes, it works, since u is a variable, you are not assuming any relationship between x and y.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook