Pertanyaan

Tentukan nilai limit berikut. x → + 4 m u y lim ( x 3 − x y 2 x 4 − y 4 )

Tentukan nilai limit berikut.

$x \to + 4 m u y lim (\frac{x ^{4} - y ^{4}}{x ^{3} - x y ^{2}})$

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

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Pembahasan

Mencari nilai limit: Jadi, .

Mencari nilai limit:

$limit as x rightwards arrow thin space y of open parentheses fraction numerator x to the power of 4 minus y to the power of 4 over denominator x cubed minus x y squared end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator open parentheses x squared close parentheses squared minus open parentheses y squared close parentheses squared over denominator x cubed minus x y squared end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator open parentheses x squared plus y squared close parentheses open parentheses x squared minus y squared close parentheses over denominator x cubed minus x y squared end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator open parentheses x squared plus y squared close parentheses open parentheses x plus y close parentheses open parentheses x minus y close parentheses over denominator x open parentheses x squared minus y squared close parentheses end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator open parentheses x squared plus y squared close parentheses open parentheses x plus y close parentheses open parentheses x minus y close parentheses over denominator x open parentheses x plus y close parentheses open parentheses x minus y close parentheses end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator open parentheses x squared plus y squared close parentheses open parentheses x minus y close parentheses over denominator x open parentheses x minus y close parentheses end fraction close parentheses equals limit as x rightwards arrow thin space y of open parentheses fraction numerator x squared plus y squared over denominator x end fraction close parentheses equals fraction numerator y squared plus y squared over denominator y end fraction equals fraction numerator 2 y squared over denominator y end fraction equals 2 y$

Jadi, $limit as x rightwards arrow thin space y of open parentheses fraction numerator x to the power of 4 minus y to the power of 4 over denominator x cubed minus x y squared end fraction close parentheses equals 2 y$ .