QJEEM20Mac60b: JEE Main 2020 Mathematics - Class 12 JEEM20Mac60b Solution: lim x → 2 ⁡ 3 x + 3 3 − x − 12 3 − x / 2 − 3 1 − x is equal…

Question

Verified Solution • 2025–26 Session moderate

lim_{x \to 2} \frac{3^{x} + 3^{3 - x} - 12}{3^{- x / 2} - 3^{1 - x}}

is equal to_______.

Accepted Answer

lim_{x \to 2} \frac{3^{x} + 3^{3 - x} - 12}{3^{- x / 2} - 3^{1 - x}}

let 3^x/2 = t

=

lim_{t \to 3} \frac{t^{2} + \frac{27}{t^{2}} - 12}{\frac{1}{t} - \frac{3}{t^{2}}}

=

lim_{t \to 3} \frac{(t^{2} - 9) (t^{2} - 3)}{t - 3}

=

lim_{t \to 3} (t + 3) (t^{2} - 3)

= 6

\times

6

= 36

Step-by-Step Verified Solution