Pertanyaan

x → 0 lim 4 x 2 tan 2 x = ...

$x \to 0 lim \frac{tan ^{2} x}{4 x ^{2}}$ = ...

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Jawaban terverifikasi

Jawaban

nilai adalah

nilai $limit as x rightwards arrow 0 of fraction numerator tan squared space x over denominator 4 x squared end fraction$ adalah 1 fourth

Pembahasan

Pada limit fungsi trigonometri untuk , berlaku sehingga Jadi, nilai adalah

Pada limit fungsi trigonometri untuk x rightwards arrow 0 , berlaku

$limit as x rightwards arrow 0 of fraction numerator a x over denominator tan space b x end fraction equals limit as x rightwards arrow 0 of fraction numerator tan space a x over denominator b x end fraction equals a over b$

sehingga

$limit as x rightwards arrow 0 of fraction numerator tan squared space x over denominator 4 x squared end fraction equals limit as x rightwards arrow 0 of fraction numerator tan space x. tan space x over denominator 4 x. x end fraction space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of fraction numerator tan space x over denominator 4 x end fraction. limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x end fraction space space space space space space space space space space space space space space space space space space equals 1 fourth.1 over 1 space space space space space space space space space space space space space space space space space space equals 1 fourth$

Jadi, nilai $limit as x rightwards arrow 0 of fraction numerator tan squared space x over denominator 4 x squared end fraction$ adalah 1 fourth