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Pertanyaan

limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x squared plus 5 x end fraction = ...

Pembahasan Soal:

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 penyelesaiannya adalah sebagai berikut :

table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x squared plus 5 x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x open parentheses x plus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x end fraction times limit as x rightwards arrow 0 of fraction numerator 1 over denominator open parentheses x plus 5 close parentheses end fraction end cell row blank equals cell 1 over 1 times 1 fifth end cell row blank equals cell 1 fifth end cell end table 

Jadi, nilai dari limit as x rightwards arrow 0 of fraction numerator tan space x over denominator x squared plus 5 x end fraction adalah 1 fifth 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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