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: Limit question

  1. Oct 9, 2011 #1
    Problem:

    Lim sin(cos(x))/sec(x)
    x -> 0

    The answer in the book is sin(1).. which is obvious... but why do I not arrive at the same answer doing is this way.....

    Knowing as x approaches zero, sin(x)/x approaches 1....

    ( Sin(cos(x))/cos(x) )(cos^2(x)) = (1)(1) = 1 = / = sin(1)...???
     
  2. jcsd
  3. Oct 9, 2011 #2

    gb7nash

    User Avatar
    Homework Helper

    The bolded part is correct. However, what is cos(x) approaching as x approaches 0?
     
  4. Oct 9, 2011 #3
    cos(x) approaches 1..
     
  5. Oct 9, 2011 #4

    gb7nash

    User Avatar
    Homework Helper

    Ok, so since cos(x) goes to 1:

    [tex]\lim_{x \to 0} \frac{\sin(\cos(x))}{\cos(x)}[/tex]

    is equivalent to:

    [tex]\lim_{u \to 1} \frac{\sin(u)}{u}[/tex]

    We can't apply the sin(_)/_ rule here. The term inside of the sine approaches 1.
     
  6. Oct 9, 2011 #5
    Thank you.
     
  7. Oct 9, 2011 #6
    I wasn't aware that you can't use that rule if the function actually approaches a value.
     
  8. Oct 9, 2011 #7

    gb7nash

    User Avatar
    Homework Helper

    [tex]\lim_{x \to 0}\frac{\sin(x)}{x} = 1[/tex]

    x needs to approach 0. If it approaches any other value (or does not exist), you can't use this identity.
     
  9. Oct 9, 2011 #8
    that makes sense. Thank you.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook