The value of  is equal to:

Concept:​

• .
• .
• .
• .

Indeterminate Forms: Any expression whose value cannot be defined, like , , 0⁰, ∞⁰ etc.

• For the indeterminate form , first try to rationalize by multiplying with the conjugate, or simplify by cancelling some terms in the numerator and denominator. Else, use the L'Hospital's rule.
• L'Hospital's Rule: For the differentiable functions f(x) and g(x), the , if f(x) and g(x) are both 0 or ±∞ (i.e. an Indeterminate Form) is equal to the  if it exists.

Calculation:

 is an indeterminate form. Let us simplify and use the L'Hospital's Rule.

.

We know that , but  is still an indeterminate form, so we use L'Hospital's Rule:

, which is still an indeterminate form, so we use L'Hospital's Rule again:

, which is still an indeterminate form, so we use L'Hospital's Rule again:

.

∴ .