If y(x)=|x|-3, "find"lim(xrarr3)f(x)....

If `y(x)=|x|-3, "find"lim_(xrarr3)f(x).`

Text Solution

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The correct Answer is:

`lim_(xto3^(+))f(x)=limf(3+h)=lim_(hto0){|3+h|-3}=lim_(hto0)(3+h-3)=lim_(hto0)h=0.`
`lim_(xto3^(-))f(x)=lim_(hto0)f(3-h)=lim_(hto0){|3-h|-3}=lim_(hto0)(3-h-3)=lim_(hto0)(-h)=0.`
`thereforelim_(xto3^(+))f(x)=lim_(xto3^(-))f(x)=0implieslim_(xto3)f(x)=0.`

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RS AGGARWAL-LIMIT-EXERCISE 27C

If y(x)=|x|-3, "find"lim(xrarr3)f(x).
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Show that lim(xrarr2)(x)/([x]) does not exist.
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