Try this beautiful problem on Sign change, useful for ISI B.Stat Entrance.
Sign change | ISI B.Stat Entrance | Problem 709
In the interval \((-2\pi, 0)\) the function \(f(x) = sin(1/x^3)\)
- (a) never changes sign
- (b) changes sign only once
- (c) changes sign more than once, but a finite number of times
- (d) changes sign infinite number of times
Check the Answer
But try the problem first…
TOMATO, Problem 709
Challenges and Thrills in Pre College Mathematics
Try with Hints
As x becomes \(\leq 1\) and tends to zero then it crosses \(\pi, 2\pi, 3\pi, ….\).can you draw the graph?
Can you now finish the problem ……….
If we draw the graph then we can see that the function \(f(x) = sin(1/x^3)\) crosses many times. Therefore number of sign changes is infinite.
Therefore option \((d)\) is correct…..
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