Discontinuous?

Geometry Level 4

f ( x ) = lim ⁡ n → ∞ x ( 2 sin ⁡ x ) 2 n + 1 \large {f(x)= \displaystyle \lim_{n \to \infty} \dfrac{x}{(2\sin x)^{2n}+1}}

How many values of x x are there from 0 0 to 9 π 2 \frac{9\pi}{2} (both inclusive) such that f ( x ) f(x) is discontinuous at those values of x x .


The answer is 9.

View wiki
Tanishq Varshney by Tanishq Varshney , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Otto Bretscher
May 30, 2015

Great problem! Thanks! f ( x ) = x if ∣ sin ⁡ x ∣ < 1 2 , f ( x ) = 0 if ∣ sin ⁡ x ∣ > 1 2 , f(x)=x\quad \mbox{if} \quad |\sin{x}|<\frac{1}{2},\quad\quad f(x)=0\quad \mbox{if} \quad |\sin{x}|>\frac{1}{2}, f ( x ) = x 2 if ∣ sin ⁡ x ∣ = 1 2 . f(x)=\frac{x}{2}\quad \mbox{if} \quad |\sin{x}|=\frac{1}{2}. Thus f ( x ) f(x) is discontinuous iff ∣ sin ⁡ x ∣ = 1 2 |\sin{x}|=\frac{1}{2} . Since there is one such point in each of the nine quadrants we consider, the answer is 9 . \boxed{9}.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

What, how does f(X) = X if |sinx|<1/2 ?

A Former Brilliant Member - 3 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...