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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

_ x → 2 3 ^ x + 3 ^ 3 - x - 12 3 ^ - (x)/(2) - 3 ^ 1 - x is equal to

lim⁡x→23x+33−x−123−x2−31−x\lim_{x \to 2}\dfrac{{3}^{x} + {3}^{3 - x} - 12}{{3}^{- \dfrac{x}{2}} - {3}^{1 - x}} is equal to

Correct answer

36

Step-by-step solution

Let, 3x2=t,x→2⇒t→33\dfrac{x}{2} = t, x \to 2 ⇒ t \to 3

lim⁡t→3t227t2−121t−3t2=lim⁡t→3t4+27−12t2t−3\lim_{t \to 3}\dfrac{{t}^{2}\dfrac{27}{{t}^{2}} - 12}{\dfrac{1}{t} - \dfrac{3}{{t}^{2}}} = \lim_{t \to 3}\dfrac{{t}^{4} + 27 - 12{t}^{2}}{t - 3}

lim⁡t→3(t2−3)(t+3)(t−3)(t−3)=6×6=36\lim_{t \to 3}\dfrac{\left({t}^{2} - 3\right)\left(t + 3\right)\left(t - 3\right)}{\left(t - 3\right)} = 6 \times 6 = 36

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