l i m x → 2 3 x + 3 3 - x - 12 3 - x 2 - 3 1 - x is equal to

Let, 3 x 2 = t , x → 2 ⇒ t → 3 lim t → 3 t 2 + 27 t 2 - 12 1 t - 3 t 2 = lim t → 3 t 4 + 27 - 12 t 2 t - 3 lim t → 3 t 2 - 3 t + 3 t - 3 t - 3 = 6 × 6 = 36

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsAlgebraic and Rational LimitsEasy2 minPYQ_2020

MathematicsEasynumerical

$\underset{x \to 2}{l i m} \frac{3^{x} + 3^{3 - x} - 12}{3^{- \frac{x}{2}} - 3^{1 - x}}$ is equal to

Answer:

36.00

Solution:

Let, $3^{\frac{x}{2}} = t, x \to 2 \Rightarrow t \to 3$

$\lim_{t \to 3} \frac{t^{2} + \frac{27}{t^{2}} - 12}{\frac{1}{t} - \frac{3}{t^{2}}} = \lim_{t \to 3} \frac{t^{4} + 27 - 12 t^{2}}{t - 3}$

$\lim_{t \to 3} \frac{(t^{2} - 3) (t + 3) (t - 3)}{(t - 3)} = 6 \times 6 = 36$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Algebraic and Rational Limits

⏱ 2mℹ️ Source: PYQ_2020

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