lim x → 0 √x^2+100 - 10/x^2 will be?

Does not exist

1/20

∞

None of these

To evaluate the limit:

lim (x→0) (√(x^2+100) - 10)/x^2

Rationalize the numerator:

= lim (x→0) ((x^2+100) - 100) / (x^2(√(x^2+100) + 10))

= lim (x→0) x^2 / (x^2(√(x^2+100) + 10))

Cancel x^2:

= lim (x→0) 1 / (√(x^2+100) + 10)

As x→0, √(x^2+100) → √100 = 10:

= 1 / (10 + 10)

= 1 / 20