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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