Question

Limit x tends to pi/2 cotx - tanx/(6x - pi)cube

Answer 1

You asked $\bold{\lim_{x\to \pi/2} \frac{cotx-tanx}{(6x-\pi)^3}}$
Let's check the form of limit ,
Put x = π/2
LHS = cotπ/2 - tanπ/2 = 0 - ∞ = -∞
RHS = (6x - π)³ = (6 × π/2 - π)³ = 4π²
LHS/RHS = -∞/4π²≠ form of limit

Hence, line doesn't exist