This Famous Limit Has a Surprising Sibling! || Why sin(x)/x Becomes 0 as x→∞ (Not 1) || HSC LIMIT

We all know the classic limit:

lim
⁡
𝑥
→
0
sin
⁡
𝑥
𝑥
=
1
x→0
lim
​

x
sinx
​
=1
But what happens when x tends to infinity?

In this video, we explore the lesser-known but fascinating limit:

lim
⁡
𝑥
→
∞
sin
⁡
𝑥
𝑥
x→∞
lim
​

x
sinx
​

Does it stay 1? Does it diverge? Or does it go to 0? 🤯
We break it down with clear explanations using the Squeeze Theorem, bounded function logic, and intuitive analogies to help you visualize and deeply understand the concept.

Perfect for high school, HSC, or first-year university students who want to boost their calculus intuition.

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[আল_ইশিগামি_সেনকু]

The sine function is bounded as:
-1 ≤ sinx ≤ 1
=> -1/x ≤ sinx/x ≤ 1/x

As x-> ∞, -1/x -> 0
As x-> ∞, 1/x -> 0
Therefore,
By Squeeze theorem,
sinx/x -> 0