Evaluating the Limit of sinx/x Approaching 0 using L’Hopital’s Rule and the Squeeze Theorem in Math.

limit as x approaches 0: sinx/x

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To evaluate the limit of sinx/x as x approaches 0, we can use L’Hopital’s rule or the Squeeze theorem.

Using L’Hopital’s rule:

lim x->0 sinx/x = lim x->0 (cosx/1) = cos(0)/1 = 1

Alternatively, we can use the Squeeze theorem. Since -1 ≤ sinx ≤ 1 for all values of x, we have:

-1/x ≤ sinx/x ≤ 1/x, as x > 0.

Taking the limits of both sides as x approaches 0 gives:

lim x->0 -1/x ≤ lim x->0 sinx/x ≤ lim x->0 1/x

As the limit on the right-hand side approaches infinity, and the limit on the left-hand side approaches negative infinity, the limit of sinx/x as x approaches 0 is equal to 1.

Therefore, the limit of sinx/x as x approaches 0 is equal to 1.

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