If f(x)=3x+2−819x−81 is continuous at x=2, then f(2)=

f(2)=Ltx→2f(x) =Ltx→23x+2−819x−81(00form)using L'hospital's rule=Ltx→23x+2log39xlog9=34 log392(2log3)=12

If f(x)=3x+2−819x−81 is continuous at x=2, then f(2)=

f(2)=Ltx→2f(x) =Ltx→23x+2−819x−81(00form)using L'hospital's rule=Ltx→23x+2log39xlog9=34 log392(2log3)=12

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If $f (x) = \frac{3^{x + 2} - 81}{9^{x} - 81}$ is continuous at $x = 2,$ then $f (2) =$

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$\frac{1}{3}$

$\frac{1}{2}$

answer is D.

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Detailed Solution

$f (2) = \underset{x \to 2}{L t} f (x)$

$= \underset{x \to 2}{L t} \frac{3^{x + 2} - 81}{9^{x} - 81} (\frac{0}{0} f o r m)$

using L'hospital's rule

$= \underset{x \to 2}{L t} \frac{3^{x + 2} \log 3}{9^{x} \log 9} = \frac{3^{4} \log 3}{9^{2} (2 \log 3)} = \frac{1}{2}$

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If f(x)=3x+2−819x−81 is continuous at x=2, then f(2)=

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If $f (x) = \frac{3^{x + 2} - 81}{9^{x} - 81}$ is continuous at $x = 2,$ then $f (2) =$