# Discuss the Continuity of the Function F at X = 0 - Mathematics

Sum

Discuss the continuity of the function f at x = 0

If f(x) = (2^(3x) - 1)/tanx, for x ≠ 0

= 1,   for x = 0

#### Solution

Given f(0) = 1

Consider,

lim_(x->0) f (x) = lim_(x->0) [(2^(3x) - 1)/tanx]

= lim_(x->0) [((2^(3x) - 1)/x)/((tanx)/x]], x ≠ 0

= lim_(x->0) [(2^(3x) - 1)/(3x).3]/(lim_(x->0)(tanx)/x) = 3 log 2

= log 8

(lim_(x->0) (a^x - 1)/x = log a and lim_(x->0) (tan x)/x = 1)

as x -> 0, 3x ->0

Since (lim_(x->0) f(x) ≠ f(0)

f(x) is discontinuous at x = 0

Concept: Continuous Function of Point
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