Question

Determine if f defined by f(x) = \(\begin{cases} x^2sin\frac{1}{x}, \; if \; x \neq0 \\ 0, \; if\; x = 0 \end{cases}\)is a continuous functions ?

Answer 1

Let a ∈ R where R is the domain of f(x)

Hence the function is continous when a ≠ 0 

Let a = 0 f(x) = 0 

∴ function is continuous at x = 0 

∴ f is continuous every where.