Pertanyaan

Jika L , K adalah bilangan real dan x → c lim f ( x ) = L , x → c lim g ( x ) = K maka tentukan x → c lim f 2 ( x ) + L 2 f 2 ( x ) − L 2 !

Jika $L$ , $K$ adalah bilangan real dan $x \to c lim f (x) = L$ , $x \to c lim g (x) = K$ maka tentukan $x \to c lim \frac{f ^{2} ( x ) - L ^{2}}{f ^{2} ( x ) + L ^{2}}$ !

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Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f squared open parentheses x close parentheses minus L squared over denominator f squared open parentheses x close parentheses plus L squared end fraction equals 0 end style$ .

Pembahasan

Dengan menggunakan sifat berikut: 1. ; 2. ; 3. ; dan 4. . maka diperoleh: Dengan demikian, .

Dengan menggunakan sifat berikut:

1. $begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator limit as x rightwards arrow c of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow c of g left parenthesis x right parenthesis end fraction end style$ ;

2. ;

3. ; dan

4. .

maka diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow c of fraction numerator f squared open parentheses x close parentheses minus L squared over denominator f squared open parentheses x close parentheses plus L squared end fraction end cell equals cell fraction numerator limit as x rightwards arrow c of open parentheses f squared open parentheses x close parentheses minus L squared close parentheses over denominator limit as x rightwards arrow c of open parentheses f squared open parentheses x close parentheses plus L squared close parentheses end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow c of f squared open parentheses x close parentheses minus limit as x rightwards arrow c of L squared over denominator limit as x rightwards arrow c of f squared open parentheses x close parentheses plus limit as x rightwards arrow c of L squared end fraction end cell row blank equals cell fraction numerator open parentheses limit as x rightwards arrow c of f left parenthesis x right parenthesis close parentheses squared minus open parentheses limit as x rightwards arrow c of L close parentheses squared over denominator open parentheses limit as x rightwards arrow c of f left parenthesis x right parenthesis close parentheses squared plus open parentheses limit as x rightwards arrow c of L close parentheses squared end fraction end cell row blank equals cell fraction numerator L squared minus L squared over denominator L squared plus L squared end fraction end cell row blank equals cell fraction numerator 0 over denominator 2 L squared end fraction end cell row blank equals 0 row blank blank blank row blank blank blank row blank blank blank row blank blank blank end table end style$

Dengan demikian, $begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f squared open parentheses x close parentheses minus L squared over denominator f squared open parentheses x close parentheses plus L squared end fraction equals 0 end style$ .

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