Pertanyaan

Nilai x → 0 lim x tan x 2 sin 2 5 x = …

Nilai $x \to 0 lim \frac{2 sin ^{2} 5 x}{x tan x} = \dots$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Perhatikan perhitungan berikut! Jadi, . Oleh karena itu, jawaban yang benar adalah C.

Perhatikan perhitungan berikut!

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator 2 space sin squared space 5 x over denominator x space tan space x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 space sin space 5 x space sin space 5 x over denominator x space tan space x end fraction end cell row blank equals cell open parentheses limit as x rightwards arrow 0 of 2 close parentheses open parentheses limit as x rightwards arrow 0 of fraction numerator sin space 5 x over denominator x end fraction times 5 over 5 close parentheses open parentheses limit as x rightwards arrow 0 of fraction numerator sin space 5 x over denominator tan space x end fraction close parentheses end cell row blank equals cell 2 open parentheses 5 limit as x rightwards arrow 0 of fraction numerator sin space 5 x over denominator 5 x end fraction close parentheses open parentheses limit as x rightwards arrow 0 of fraction numerator sin space 5 x over denominator tan space x end fraction close parentheses end cell row blank equals cell 2 cross times 5 cross times 5 end cell row blank equals 50 end table$

Jadi, $limit as x rightwards arrow 0 of fraction numerator 2 space sin squared space 5 x over denominator x space tan space x end fraction equals 50$ .

Oleh karena itu, jawaban yang benar adalah C.