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lim x→π/4 (cot³ x − tan x) / cos(x + π/4) is:

1. 8√2
2. 4
3. 4√2
4. 8

Correct answer: 8

Solution

As x approaches π/4, cot³(x) approaches 1 and tan(x) also approaches 1, making the numerator approach 0. The denominator, cos(x + π/4), approaches 0 as well, leading to an indeterminate form. Applying L'Hôpital's Rule, we differentiate the numerator and denominator, ultimately simplifying to find that the limit evaluates to 8.

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