Question

limit x tends to 0 is sin x cos x by 3x​

Answer 1

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$\: \: \gg \boxed{ \bf{answer}}$

$\bullet\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}$

$\: \: \gg:\large \boxed{ \sf{properties}}$

$\: \bullet \displaystyle \bf{ \frac{sinx}{x} = 1 \: at \: x \: tends \: to \: 0 \: only}$

$\: \bullet \displaystyle \bf{ \frac{cosx}{x} = 1 \: if \: x \: tends \: to \: 0 \: only}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{cosx}{x} \dfrac{sinx}{3}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: 1\times \dfrac{sinx}{3}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinx}{3}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sin0\degree}{3}}$

$\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{1}{3}}$

$\divideontimes\boxed{\displaystyle\bf{lim_x\to0 \: \ggg\dfrac{1}{3} \: is\: the\: \:correct\: answer}}$