To find: \(\lim\limits_{\text x \to0}\cfrac{sin(2+\text x)- sin (2 -\text x)}{\text x}\)
We know,
Therefore,
Formula used:
= 2 cos 2 × 1
= 2 cos 2
Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sin(2+\text x)- sin (2 -\text x)}{\text x}\) = 2 cos 2