If f(x) = (e^(x^2) - cos x)/x^2, for x ≠ 0 is continuous at x = 0, find f(0).

Question

i. If f(x) = \(\frac{e^{x^2}-cos\,x}{x^2},\) for \(x \neq 0\) is continuous at x = 0, find f(0).

(e^{x^2} - cos x)/x²,

ii. If f(x) = \(\frac{1 - cos[7(x - \pi)]}{5(x - \pi)^2},\)  for \(x \neq \pi\) is continuous at x = π, find f(π).

Answer 1

i. f is continuous at x = 0.