Where are each of the following functions discontinuous? f(x) = x2 - 3x - 18/x -

Question

Where are each of the following functions discontinuous? f(x) = x2 - 3x - 18/x - 6 f(x) = 1/x5 if x 0 1 if x = 0 f(x) = x2-3x-18/x-6 if x 6 1 if x = 6 f(x) = [[x]] Notice that f(6) is not defined, so f is discontinuous at Later we'll see why f is continuous at all other numbers. Here f(0) = is defined, but lim x rightarrow 0 f(x) = lim x rightarrow 0 1/x5 is defined, but does not exist. So f is discontinuous at Here f(6) = is defined and exists. But lim x rightarrow 0 f(x) f(6) so f is not continuous at The greatest integer function f(x) = [[x]] has discontinuities at all the integers because the limit as x approaches n of f(x) does not exist if n is an integer.

Explanation / Answer

a. x=6

b. f(0) = 1. f is discontinuous at x=0

c.f(6)=1.

(x+3) and the next blank limit = (6+3) =9.

f is not continuous at x=6

d. Discontinuous at all integers. Since, the limit as x approaches an integer is equal to the previous integer.

limit at x=3 from left = 2

limit at x=3 from right = 3

Hence, discontinuous at all integers,

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