Question

lim x->0 (sqrt1+2x-sqrt1-4x) /x use hospitals rule

Answer 1

\[\lim_{x \rightarrow 0}\frac{ \sqrt{1+2x}-\sqrt{1-4x} }{ x}\]

Answer 2

does the question ask you to use the L'Hopital's rule? you can solve this without that

Answer 3

As x approaches zero then I get:
\[\frac{ 0 }{ 0}\] Therefore l'Hopital's rule is used. By differentiating I get\[\frac{ 2 }{ \sqrt{1-4x}}+\frac{ 1 }{ \sqrt{1+2x}}\]So the answer is:\[\lim_{x \rightarrow 0}\frac{ \sqrt{1+2x}-\sqrt{1-4x}}{ x}=\lim_{x \rightarrow 0}\frac{ 2 }{ \sqrt{1-4x} }+\frac{ 1 }{ \sqrt{1+2x} }=3\]Hope I helped, gimme a medal to lemme know!

Answer 4

thank u :)