Question

Find the vaule of:

lim x approaches 0: (x^2+x)/(2*sqrt(x^3+x^2))

Answer 1

factor out the numerator and then denominator.

x^2 + x = x(x+1)
and
2*sqrt(x^3+x^2) = 2 sqrt(x^2(x+1)) = 2x sqrt(x+1)
then you can cancel the x's

Answer 2

Do we know if we are approaching from the right or from the left? If we don't then \(\sqrt{x^{2}} = |x|\). It makes quite a difference when playing around zero (0).

Answer 3

This helped, thank you.

Answer 4

the question didnt state left or right.

Answer 5

just lim as x approaches 0.

Answer 6

With no clarification from the problem statement, you must consider each case separately.

|x| = x for \(x \ge 0\)
|x| = -x for \(x < 0\)