Pertanyaan

x → 0 lim tx ⋅ sin 2 x 1 − cos x = ....

$x \to 0 lim \frac{1 - cos x}{tx \cdot sin 2 x} = ....$

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Jawaban terverifikasi

Jawaban

hasil limit tersebut adalah .

hasil limit tersebut adalah $fraction numerator 1 over denominator 4 t end fraction$ .

Pembahasan

Ingat kembali: Maka: Jadi, hasil limit tersebut adalah .

Ingat kembali:

1 minus cos space straight x equals 2 times sin squared open parentheses 1 half straight x close parentheses

Maka:

$limit as straight x rightwards arrow 0 of space fraction numerator 1 minus cos space straight x over denominator tx times sin space 2 straight x end fraction equals limit as straight x rightwards arrow 0 of space fraction numerator 2 times sin squared open parentheses begin display style 1 half straight x end style close parentheses over denominator tx times sin space 2 straight x end fraction space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow 0 of space fraction numerator 2 times sin space open parentheses begin display style 1 half straight x end style close parentheses times sin space open parentheses begin display style 1 half straight x end style close parentheses over denominator tx times sin space 2 straight x end fraction space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow 0 of space 2 over straight t times fraction numerator sin space open parentheses begin display style 1 half straight x end style close parentheses over denominator straight x end fraction times fraction numerator sin space open parentheses begin display style 1 half straight x end style close parentheses over denominator sin space 2 straight x end fraction space space space space space space space space space space space space space space space space space space space space space space equals 2 over straight t times 1 half times fraction numerator begin display style 1 half end style over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space space space equals 2 over straight t times 1 half times 1 fourth space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator 8 straight t end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator 4 straight t end fraction space space space space space space space space space space space space space space space space space space space space space space$

Jadi, hasil limit tersebut adalah $fraction numerator 1 over denominator 4 t end fraction$ .