What is the limit where $lim_(x → 0) (sqrt(a+x) - sqrta)/(xsqrt(a(a+x)$ ?

Question

$(sqrt(a+x) - sqrta)/(xsqrt(a(a+x))$

1248 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-09T15:28:34

$L=sqrta/(2a^2)$

Here,

$L=lim_(xto0) (sqrt(a+x)-sqrta)/(xsqrt(a(a+x))$

$=lim_(xto0) (sqrt(a+x)- sqrta)/(xsqrt(a(a+x)))xx(sqrt(a+x)+sqrta)/(sqrt(a+x)+sqrta)$

$=lim_(xto0) (cancela+x- cancela)/(xsqrt(a(a+x)))xx1/(sqrt(a+x)+sqrta$

$=lim_(xto0)cancelx/(cancelxsqrt(a(a+x))(sqrt(a+x)+sqrta)$

$=lim_(xto0)1/(sqrt(a(a+x))(sqrt(a+x)+sqrta)$

$=1/(sqrt(a(a+0))*(sqrt(a+0)+sqrta)$

$=1/(sqrt(a^2)(sqrta+sqrta)$

$=1/(a(2sqrta)$

$=sqrta/(2a^2)$