## lim x->0 sinx/x

### The given expression lim x->0 sinx/x represents the limit of the function (sin(x))/x as x approaches 0

The given expression lim x->0 sinx/x represents the limit of the function (sin(x))/x as x approaches 0.

To find this limit, we can approach it by simplifying the expression. Recall the trigonometric identity:

lim θ->0 sinθ/θ = 1

Using this identity, let’s rewrite our expression:

lim x->0 sinx/x = 1

Therefore, the limit of (sin(x))/x as x approaches 0 is equal to 1.

Further Explanation:

This limit is a fundamental result in calculus and has several important applications. It is often encountered when dealing with derivatives and integrals of trigonometric functions. The fact that the limit is equal to 1 signifies that as x approaches 0, the ratio of sin(x) to x approaches 1.

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