# Sign change | ISI-B.stat | Objective Problem 709

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

### Key Concepts

Calculus

Limit

Trigonometry

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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