Find the limit, if it exists. lim x → ∞ x^3/√(x^6 + 3)

Answer 1

Hi Emanuel,

We know the limit exists since the function is a quotient of two continuous functions and is therefore continuous, provided that the denominator is not equal to zero. The limit is 1. To see this, factor x⁶ out of the square root in the bottom expression to get

lim_x→∞ x³/(√(x⁶)√(1+3/x⁶))

=lim_x→∞x³/(x³√(1+3/x⁶))

=lim_x→∞1/√(1+3/x⁶)

=1/√(1+0)

=1.

Hope that helped.