#25 Measure Your Calibre

Calculus Level pending

A problem was given by Akeel Howell , Here you get it Complex Limit

Here he says that to find \[\large \lim_{t \to \infty}{\int_{0}^{\ln{t}}{\cos{(ix)}} \, dx} =\ \dfrac{a}{b}t \]

Now 1st of all we need \(\cos (ix)\)

So Initially what i did was this

Step 1 \(\cos(ix)\) = \(Re(e^{i \times (ix)})\) By Euler's Method

Step 2 So I got \(Re(e^{-x})\)

Step 3 Then as \(e^{-x}\) is Fully real so \(Re(e^{-x}) = e^{-x} = \cos(ix)\)

Step 4 But we know \(\cos (ix) = coshx = \dfrac{e^x+e^{-x}}{2}\)

So whats wrong in evaluating \(\cos (ix)\)?

Input your answer as the step number. If you think whole thing is wrong input \(10\) but give reason.


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