JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(f(x)=\left\{\begin{array}{cc}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ a \log _e 2 \log _e 3 & , x=0\end{array}\right.\) is continuous at \(x=0\), then the value of \(a^2\) is equal to
- A \(968\)
- B \(1152\)
- C \(746\)
- D \(1250\)
Answer & Solution
Correct Answer
(B) \(1152\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0} f(x)=a \ln 2 \ln 3 \) \( \lim _{n \rightarrow 0} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}=\lim _{x \rightarrow 0} \frac{\left(8^x-1\right)\left(9^x-1\right)}{\sqrt{2}-\sqrt{1+\cos x}} \)…
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