limit x tends to 0 is sin x cos x by 3x
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[tex] \: \: \gg \boxed{ \bf{answer}}[/tex]
[tex]\bullet\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}[/tex]
[tex] \: \: \gg:\large \boxed{ \sf{properties}}[/tex]
[tex] \: \bullet \displaystyle \bf{ \frac{sinx}{x} = 1 \: at \: x \: tends \: to \: 0 \: only}[/tex]
[tex] \: \bullet \displaystyle \bf{ \frac{cosx}{x} = 1 \: if \: x \: tends \: to \: 0 \: only}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinxcosx}{3x}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{cosx}{x} \dfrac{sinx}{3}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: 1\times \dfrac{sinx}{3}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sinx}{3}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{sin0\degree}{3}}[/tex]
[tex]\implies\displaystyle\tt{lim_x\to0 \: \: \dfrac{1}{3}}[/tex]
[tex]\divideontimes\boxed{\displaystyle\bf{lim_x\to0 \: \ggg\dfrac{1}{3} \: is\: the\: \:correct\: answer}}[/tex]