Prove the formula for the limit:

Using,

* Proof. * First, since we have

Then, we use the formula (from Apostol, Theorem 2.3 (f)), with and in place of and ,

But, from a previous exercise (Section 3.6, #15) we know , so

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Stumbling Robot

A Fraction of a Dot
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Establish the given limit formula

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Prove the formula for the limit:

Using,

* Proof. * First, since we have

Then, we use the formula (from Apostol, Theorem 2.3 (f)), with and in place of and ,

But, from a previous exercise (Section 3.6, #15) we know , so

It’s just the sine double angle identity: sin(2x)=2sin(x)cos(x). Except replace 2x with 4x.

Yes. As in Exercise 16, we can do without the special limit (i.e., (sin x)/x approaches 1 as x approaches 0).

sin(4x)+cos(x)+sinxcos(4x)/x. after this line iam not getting which formula you applied to proceed to next line will you please ellaborate with formula mentioned.