1. Not finding help here? Sign up for a free 30min 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!

Limits of trigonometric functions

  1. Jul 6, 2008 #1
    1. The problem statement, all variables and given/known data

    lim x --->0 [tan(2+x)^3 - tan8]/x

    2. Relevant equations

    f'(a)=lim h-->0 f(a+h)-f(a)/h

    3. The attempt at a solution

    should i differentiate first? am i allowed to do that?
     
    Last edited: Jul 6, 2008
  2. jcsd
  3. Jul 6, 2008 #2
    f(a)=tan8
    f(a+h)=tan(x+2)^3
    h= x
    a+h=2+x=2+h so a= 2
    f(a)=f(2)=tan8
    f(x)=tanx^3
    f(2)=tan2^3=tan8
    f'(x)=secx^2 * 3x
    f'(2)= sec2^2 * 6= 6sec4
     
  4. Jul 6, 2008 #3
    does this all look correct?
     
  5. Jul 6, 2008 #4
    What book are you using? Chapter and problem number?
     
  6. Jul 6, 2008 #5
    it a problem for a test, i just need to evaluate the limit above, this is what the teacher showed to do for a similar problem
     
  7. Jul 6, 2008 #6
    Ok then, you can help yourself! You're given a take home exam ... use your book.
     
  8. Jul 6, 2008 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    First write the problem correctly. Is it
    [tex]\lim_{x\rightarrow 2}\frac{tan^3(2+x)- tan(8)}{x}[/tex]
    or is it
    [tex]\lim_{x\rightarrow 2}\frac{tan((2+x)^3)- tan(8)}{x}[/tex]

    If it is the second then it can be interpreted as the derivatve of tan(x3) at x= 2. What is that derivative? (it is NOT sec2(x^2) (3x)[. Use the chain rule.)
     
  9. Jul 6, 2008 #8
    the second one is right. but as x goes to 0
     
  10. Jul 6, 2008 #9
    sec^2(x^3)(3x)
     
  11. Jul 6, 2008 #10
    i think that is right and then i just substitute in 2 right? so its
    6sec^2(8)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limits of trigonometric functions
Loading...