Pertanyaan

x → ∞ lim x 2 ⋅ sin 2 ( x 2 )

$x \to \infty lim x^{2} \cdot sin^{2} (\frac{2}{x})$

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Jawaban terverifikasi

Pembahasan

Misal . Sehingga dari Ingat bahwa sehingga

Misal 1 over x equals y space maka italic space x italic equals italic 1 over y . Sehingga dari x rightwards arrow infinity space menjadi space space y rightwards arrow 0

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

Ingat bahwa $limit as x rightwards arrow 0 of fraction numerator sin space a x over denominator b x end fraction equals a over b space$ sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as y rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin squared space open parentheses 2 y close parentheses space over denominator y squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 1 close parentheses end cell end table squared table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table$