Question

lim a-x/sqrtx-sqrta as x->a

Answer 1

\[x=u^2\]

now we have-\[\lim_{u \rightarrow \sqrt{a}}\frac{ a-u^2 }{ \sqrt{u^2}-\sqrt{a} }\]\[\lim_{u \rightarrow \sqrt{a}}\frac{ a-u^2 }{u-\sqrt{a}} \times \frac{ u+\sqrt{a} }{u+\sqrt{a} }\]\[\lim_{u \rightarrow \sqrt{a}}\frac{ (a-u^2)(u+\sqrt{a}) }{ u^2-a }\]\[\frac{ \lim_{u \rightarrow \sqrt{a}}(a-u^2)(u+\sqrt{a} }{ \lim_{u \rightarrow \sqrt{a}}(u^2-a) }\]

try doing it from here :)

Answer 2

-2 sqrt a ?

Answer 3

yes :)

Answer 4

thank you