Question

what is the limit when x approaches 0 from the left when intx

Answer 1

Lateral limits consider only a certain region of the enviroment defined by the tendency, in this case, the left side, which implies "values smaller than".
So therefore:
\[\lim_{x \rightarrow 0^-}kx\]
Will be a limit that considers all the values of x that satisfy the condition \(x<0\) or in more technical terms \(E^-((0-x),0)\) this means "an enviroment with center "0" and radius "x" on the left side.
And what are the only values on the real numberline that satisfy that \(x<0\) ?
Well those would be the negative numbers, and even infinitely close to x=0 we will have values, therefore we deduce that "x" will have negative values:
\[\lim_{x \rightarrow 0^-}k(-x)=-kx\]