Pertanyaan

x → 0 lim x tan x sin 2 x − cos x + 1 = ...

$x \to 0 lim \frac{sin ^{2} x - cos x + 1}{x tan x} = ...$

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$begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator sin squared space x minus cos space x plus 1 over denominator x space tan space x end fraction equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x minus open parentheses 1 minus 2 space sin squared space 1 half x close parentheses plus 1 end style over denominator begin display style x space tan space x end style end fraction equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x minus 1 plus 2 space sin squared space 1 half x plus 1 end style over denominator begin display style x space tan space x end style end fraction equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x plus 2 space sin squared space 1 half x end style over denominator begin display style x space tan space x end style end fraction equals limit as x rightwards arrow 0 of open parentheses fraction numerator begin display style horizontal strike sin space x end strike space. space horizontal strike sin space x end strike end style over denominator horizontal strike x space tan space x end strike end fraction plus fraction numerator 2 space horizontal strike sin space begin display style 1 half end style horizontal strike x times horizontal strike sin space begin display style 1 half end style horizontal strike x over denominator horizontal strike x space tan space x end strike end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses 1 plus 2 times 1 half times 1 half close parentheses equals 1 plus 1 half equals 3 over 2 end style$