Question

Examine the function f(x) = \(\begin{cases} \frac{tanx}{sinx}; &x \neq 0\\ 1; &x = 0 \end{cases} \) for continuity at x = 0.

Answer 1

Continuity at x = 0,

Left hand limit

At x = 0, value of function

f(0) = 1

f(0 - 0) = f(0 + 0) = f(0) = 1

Hence, at x = 0, given function f(x) is continuous.