Mastering The Squeeze Theorem To Evaluate The Limit Of Sin(Bx)/X

lim x->0 sinbx/x

b

To evaluate the limit:

lim x -> 0 sin(bx)/x

we will use the squeeze theorem.

Note that sin(bx) is bounded between -1 and 1, for all values of x. That is,

-1 ≤ sin(bx) ≤ 1 for all x.

We can multiply both sides of the inequality by 1/x (since x is positive and winding towards 0), and we get

-1/x ≤ sin(bx)/x ≤ 1/x

Now, we can take the limit as x approaches 0 for all three parts of the inequality. Using the Squeeze Theorem, we see that the limit of sin(bx)/x as x approaches 0 is equal to 0.

Thus, we have:

lim x -> 0 sin(bx)/x = 0.

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