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A day full of math games & activities. Find one near you.
Evaluate the following limits in Exercises 1 to 22: lim z→₁ (z¹/³ - 1)/(z¹/⁶ - 1)
Solution:
At z = 1, the value of the given function takes the form 0/0, which is an indeterminate form.
So we will evaluate the given limit differently.
Put z1/6 = x so that z → 1 as x → 1
Accordingly,
lim z→₁ (z1/3 - 1)/(z1/6 - 1) = lim ₓ→₁ (x2 - 1)/(x - 1)
= lim ₓ→₁ (x2 - 12)/(x - 1)
= 2 × 12 - 1 [∵ (xn - an)/(x - a) = nan - 1]
= 2
NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 10
Evaluate the following limits in Exercises 1 to 22: lim z→₁ (z¹/³ - 1)/(z¹/⁶ - 1)
Summary:
The value of the limit lim z→₁ (z1/3 - 1)/(z1/6 - 1) is 2
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