Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (( x + 1)⁵ - 1)/x

Solution:

The given limit is, limₓ→₀ ((x + 1)⁵ - 1)/x

By direct substitution of x = 0 gives 0/0 which is an indeterminate form. So we have to find this limit differently.

Put x + 1 = y , so that x = y - 1

Accordingly,

limₓ→₀ ((x + 1)⁵ - 1)/x = limᵧ→₀ (y)⁵ - 1)/(y - 1)

= 5 × (1)^{5 - 1} [∵ limₓ→₀ (xⁿ - aⁿ)/(x - a) = na^{n - 1}]

= 5

Hence,

limₓ→₀ (( x + 1)⁵ - 1)/x = 5

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 6

Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (( x + 1)⁵ - 1)/x

Summary:

The value of the limit limₓ→₀ (( x + 1)⁵ - 1)/x is 5