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))#

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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)#