`f(x)= {{:((|x-4|)/(2(x-4)), if x ne 4),(0,if x = 4):}` at `x = 4` is.

1.	`f(x)= {{:((\|x-4\|)/(2(x-4)), if x ne 4),(0,if x = 4):}` at `x = 4` is.
Answer» LHL of f(x) at x=4 is `underset(xto4^(+))limf(x)=underset(hto0)limf(4-h)` `=underset(hto0)lim(\|4-h-4\|)/(4-h-4)=underset(hto0)lim(\|-h\|)/(-h)` `=underset(hto0)limh/-h=underset(hto0)lim-1` `=-1` `RHL " of " f(x) " at "x=4" is"` `underset(xto4^(+))limf(x)=underset(hto0)limf(4+h)` `=underset(hto0)lim(\|4+h-4\|)/(4+h-4)` `=underset(hto0)lim(\|h\|)/(h)=underset(hto0)limh/h=underset(hto0)lim1` `=1`

Discussion

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