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Homework Help: Questions on trig limits?

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data
    1. sin(1/x) as x->infinity
    2. tan(7x)/sin(5x) as x->0
    3. General question--when finding the derivative (through implicit diff.), and I have something like y=(5x^2)y, what parts am I supposed to use the chain rule, and when am I supposed to use the product rule?

    3. The attempt at a solution
    1. I literally have no idea how to do this. Possibly multiplying, but sin/sinx doesn't seem to get me anywhere.
    2. sin7x/cos7x times 1/sin5x. Not quite sure what to do afterwards.
    3. Is this correct? -- 10x^2(y) times y' ?
  2. jcsd
  3. Oct 10, 2011 #2
    1: Consider what the limit of 1/x is, as x tends toward infinity. Then use that to evaluate sin(1/x) as x tends toward infinity.

    2: Consider using L'Hopital's Rule.

    3: I am not certain that I fully understand what you're asking, so I will refrain from comment.
  4. Oct 10, 2011 #3
    I'm honestly unsure how to explain this as well.
    I just need help on how to do number 3.
  5. Oct 10, 2011 #4


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    Staff Emeritus
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    Look at 1/x when x = BIG number. Try 1000, then 1000000, then 10100, etc.
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