$$\mathop {\lim }\limits_{x \to 2} {{{3^x} + {3^{3 - x}} - 12} \over {{3^{ - x/2}} - {3^{1 - x}}}}$$ is equal to_______.
Answer (integer)
36
Solution
$$\mathop {\lim }\limits_{x \to 2} {{{3^x} + {3^{3 - x}} - 12} \over {{3^{ - x/2}} - {3^{1 - x}}}}$$
<br><br>let 3<sup>x/2</sup> = t
<br><br>= $$\mathop {\lim }\limits_{t \to 3} {{{t^2} + {{27} \over {{t^2}}} - 12} \over {{1 \over t} - {3 \over {{t^2}}}}}$$
<br><br>= $$\mathop {\lim }\limits_{t \to 3} {{\left( {{t^2} - 9} \right)\left( {{t^2} - 3} \right)} \over {t - 3}}$$
<br><br>= $$\mathop {\lim }\limits_{t \to 3} \left( {t + 3} \right)\left( {{t^2} - 3} \right)$$
<br><br>= 6 $\times$ 6
<br><br>= 36
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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