What happens if you try to use l'hospital's rule to find the limit? lim x → ∞ x / x² + 5.

We will use the concept of limit in order to find the required limit.

Answer: By the l'hospital's rule, the required limit is 0.

Let us see how we will use the concept of limit in order to find the required limit.

Explanation:

The limit that has been given to us is Lim x → ∞ (x / x² + 5)

The concept of l'hospital says that differentiate the numerator and denominator, separately with respect to the variable if we have a limit of the form 0 / 0 or ∞ / ∞ .

Lim x → ∞ (x / x² + 5) = ∞ / ∞

On differentiating we get that,

lim x → ∞ (1 / 2x )

Now, if  x → ∞ in the denominator and since the numerator has 1,so denominator >> 1and 1 / ∞  = 0.

⇒ lim x → ∞ (1 / 2x ) = 0

Hence, the required limit is equal to 0.