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If $f (x) = {\begin{matrix} \frac{6^{x} - 3^{x} - 2^{x} + 1}{2 \sin^{2} (\frac{x}{2})}, & if & x \neq 0 \\ K, & if & x = 0 \end{matrix}$ is continuous at $x = 0,$ then $K =$

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detailed solution

Correct option is B

K=f(0)=Ltx→0f(x)=Ltx→0(3x−1)(2x−1)2sin2(x2) =Ltx→0(3x−1)(2x−1)x22sin2(x2)x2=log3.log22.14=2log3.log2

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If f(x)={6x−3x−2x+12sin2(x2),ifx≠0K,ifx=0 is continuous at x=0, then K=

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If $f (x) = {\begin{matrix} \frac{6^{x} - 3^{x} - 2^{x} + 1}{2 \sin^{2} (\frac{x}{2})}, & if & x \neq 0 \\ K, & if & x = 0 \end{matrix}$ is continuous at $x = 0,$ then $K =$