slope of tangent line of |x|

[heartshapes]

Use the limit definition to compute the slope of the tangent line as a limit of slopes of secant lines.

a) k(x) = |x|

ok so I know there are different limits from the left and right. I am really at the tex language so please forgive me..

lim from 0- (left) = (|c+h|-|c|)/h
lim from 0- (left) = |h|/h
is the limit from the left -1?

lim from 0+ (right) = (|c+h|-|c|)/h
lim from 0+ (right) = |h|/h
is the limit from the right 1?

so the limit doesnt exist at (0,0)?

thanks!

 

[royhaas]

Yes, the limit of the absolute value function at the origin does not exist.

 

[Pklarreich]

Yes, the limit of the absolute value function at the origin does not exist.

I think you meant to say: Yes, the limit of the slope of the tangent to the absolute value function at the origin does not exist.