Limit of a composite function!

Calculus Level 5

$\large \lim_{x\to0} \left[\lim_{n\to\infty} 2^{2n} \left(1 - f^n(x) \right)\right]$

For $f: [0,1] \rightarrow \mathbb R$ and $f(x) = \sqrt{\frac{1+x}2}$ , find the limit above.

Clarification: $f^n(x) = \underbrace{f \circ f \circ f \circ \ldots \circ f}_{n \text{ times}} (x)$ .

\dfrac{\pi^2}{8}

\dfrac{\pi^2}{6}

\pi

\dfrac{\pi^2}{4}

\dfrac{\pi^2}{2}

\pi^2

1 solution

Satyajit Mohanty
Jul 9, 2015

Oh no Check This

Ronak Agarwal - 5 years, 11 months ago

Wow! What a Co-incidence! Looks our problem sources are same, we're just twisting the problem according to Brilliant's requirements in our own fashion :D

Satyajit Mohanty - 5 years, 11 months ago

The source of mine is me myself.

What's your source. I thought it was an original problem.

Ronak Agarwal - 5 years, 11 months ago

@Ronak Agarwal – No. I solved a subjective (Prove that....) kind of problem during my JEE Prep. I just twisted it to make it into an objective pattern.

Satyajit Mohanty - 5 years, 11 months ago

@Ronak Agarwal – I don't understand how your problem is worth 335 points and mine just 155 :/

Satyajit Mohanty - 5 years, 11 months ago

Limit of a composite function!

1 solution

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