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## Main Question or Discussion Point

Does the function f(x) l x

Attempt: l x

(x

-(x

Lim x→1+ (x

Lim x→1- -(x

Therefore, it does have a limit because the right and left hand limit are equal and the slope of the tangent line is 0. Is this right? My book tells me that the same type of question but with equation f(x)=√lxl at x=0 does not have a tangent line, same with the equation f(x)=lxl at x=0. It tells me neither of those equations have a tangent line at their given points.

^{2}-1 l have a tangent line at x=1? What is the tangent line if it does?Attempt: l x

^{2}-1 l(x

^{2}-1) When x ≥ 1-(x

^{2}-1) When x < 1Lim x→1+ (x

^{2}-1) = 0Lim x→1- -(x

^{2}-1) = 0Therefore, it does have a limit because the right and left hand limit are equal and the slope of the tangent line is 0. Is this right? My book tells me that the same type of question but with equation f(x)=√lxl at x=0 does not have a tangent line, same with the equation f(x)=lxl at x=0. It tells me neither of those equations have a tangent line at their given points.