continuity

Asked by  | 24th Jul, 2008, 10:56: PM

Expert Answer:

since f(x) is a polynomial in x , and polynomials functions are continuous except at boundary points

so we should check continuity at x=2

at x=2 , f(x) = 16

but when x->2 ,f(x)  is 0/0 which is undefined.

so  by applying L.Hospital rule when x->2

f(x) = lim x->2 d/dx ( (x4-16)/ (x-2) ) = limx->2 4x3 = 32

so here limiting value and value of f(x) at x=2 are not equal so function is discontinuous at x=2.

Answered by  | 11th Aug, 2008, 06:14: PM

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