Calculus: Early Transcendentals, Chapter 2, 2.3, Section 2.3, Problem 27

lim_(x->0) (4 - sqrt(x))/(16x - x^2)
sol:
lim_(x->0) (4 - sqrt(x))/(x(16 - x))
=> lim_(x->0) (4 - sqrt(x))/(x(4^2 - (sqrt(x))^2))
=> lim_(x->0) (1)/(x(4 + (sqrt(x))))
as x-> 0
and now let us check whether
lim_(x->0^-) ((1)/(x(4 + (sqrt(x))))) is equal tolim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
so,
lim_(x->0^-) ((1)/(x(4 + (sqrt(x)))))
= (1/0^-) = -oo
and
lim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
= 1/0^+ = +oo ,
As ,lim_(x->0^-) ((1)/(x(4 + (sqrt(x))))) != lim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
so limit doesnt exist