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The function f(x)=|x| is continuous at:a) X=0 b) X is not equal to 1 c) X=E

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farahyasmin | Student, Undergraduate | (Level 1) Honors

Posted January 8, 2013 at 1:54 PM via web

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The function f(x)=|x| is continuous at:
a) X=0 b) X is not equal to 1 c) X=E

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 8, 2013 at 2:24 PM (Answer #1)

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You need to remember that a function is continuous at a value `x = x_0` if `lim_(x->x_0) |x| = f(x_0)` , hence, you need to evaluate the limit of the function at `x = 0` and you need to evaluate the value of the function at `x = 0` , and then, you need to compare the result.

You also need remind the definition of the absolute value function, such that:

`|x| = {(x, x>0),(0, x=0),(-x, x<0):}`

You need to evaluate the limit of the function such that:

`lim_(x->0) |x| = |0| = 0`

You need to evaluate the value of the function at `x` ` = 0` such that:

`f(0) = |0| = 0`

Notice that `lim_(x->0) |x| = f(0) = 0` , hence, the absolute value function is continuous at `x = 0` , thus, you need to select the answer `a) x = 0` .

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