Question

evaluate the one sided limit lim->1/3from the negative direction sqrt1-3x

Answer 1

i wanna use a good method for that... try to work it out

limit x->1/3 from the negative direction so u can write \[x=\frac{1}{3}-y\]y-->0 from positive direction now easily u can see\[\sqrt{1-3x}=\sqrt{1-3(\frac{1}{3}-y)}=\sqrt{y}\]

Answer 2

sorry\[\sqrt{1-3x}=\sqrt{1-3(\frac{1}{3}-y)}=\sqrt{3y}\]

Answer 3

now u have\[\lim_{y \rightarrow 0^+} \sqrt{3y}\]