Evaluate the following limit : lim(x→1) (1 - x^2)/(sin 2πx)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to1} \cfrac{1-\text x^2}{sin\, 2\pi\text x} \)

lim(x→1) (1 - x²)/(sin 2πx)

Answer 1

We have Given, \(\lim\limits_{\text x \to1} \cfrac{1-\text x^2}{sin\, 2\pi\text x} \)

Here, x → 1, then x – 1 → 0, let x – 1 = y

Hence, \(\lim\limits_{\text x \to1} \cfrac{1-\text x^2}{sin\, 2\pi\text x} \) = \(-\cfrac1\pi\)