Answer :

Using Rolle's theorem, we can prove that the limit of sin(x)/x as x approaches 0 is equal to 1.

Rolle's theorem states that if a function is continuous on a closed interval and differentiable on an open interval, and the function values at the endpoints of the interval are equal, then there exists at least one point in the interval where the derivative of the function is zero.

In this case, we have f(x) = sin(x) and g(x) = 1.

Both of these functions are continuous and differentiable at all points.

We know that f(0) = sin(0) = 0 and g(0) = 1.

Therefore, according to Rolle's theorem, there exists a point c such that f'(c) = g'(c) = 0.

Taking the derivative of f(x) = sin(x), we get f'(x) = cos(x). So, at the point c, we have cos(c) = 0.

We can also note that the limit of sin(x)/x as x approaches 0 is equal to 1, and the limit of cos(x)/1 as x approaches 0 is also equal to 1.

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