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Calculus/Evaluation of limit

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Expert: - 4/23/2010


Question
QUESTION: Sir,I'm totally exhausted after trying to find an answer to this Q in vain.the Q is
Lt-->0 16[1-cos(cos10x)]
      -----------------
         x^4

ANSWER: Is that lim(x->0) [(1-cos{cos(10x)})/x^4]?

The cos(0) = 1.
The top goes to 1 - cos(cos(0)), which is 1 - cos(1), which is not zero.

The bottom, x^4, goes to 0 as x->0.

This implies the limit goes to non-zero/0 -> ∞.


---------- FOLLOW-UP ----------

QUESTION: I'm sorry Mr.Scotto but the answer is 6.Would u mind trying again?please

Answer
So is that lim(x->0) [16(1-cos{cos(10x)})/x^4]?

It is known that the lim(x->0)(10x) = 10*0 = 0.
Using this, the cos(10x) would then go to the cos(0), and the cos(0) is 1.

The cos(cos(10x)) would then go to cos(1), since cos(10x) -> 1.

The cos(1) is not 0 and is not 1, but is somewhere inbetween.

This means the top is not 0, but the bottom is 0, so what I gave goes to ∞.

I may have forgot to put in the 16 before, but even with it in there,
the answer is still ∞.

So my interpretation of the problem must be wrong.
According to what I read, compute 10x first, then take the cos of that, then take the cos of that, then subtract it from 1, then multiply it by 16, and then divide by x to the fourth.

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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