Question

If f(x) = `{{:(tanx/x + secx",",   x ≠ 0),(2",",  x = 0):}`, then ______.

Options

• f(x) is discontinuous at x = 0

• `lim_(x -> 0) "f"(x)` = 1

• f(x) is continuous at x = 0

• none of these

Answer 1

If f(x) = `{{:(tanx/x + secx",",   x ≠ 0),(2",",  x = 0):}`, then f(x) is continuous at x = 0.

Explanation:

`lim_(x -> 0) "f"(x) =  lim_(x -> 0)(tanx/x + sec x)`

= 1 + 1 = 2

= f(0)

∴ f(x) is continuous at x = 0.