Jika L, K adalah bilangan real dan x→clim f(x) = L, x→clim g(x) = K maka tentukan x→climf2(x)+L2f2(x)−L2!

Pertanyaan

Jika $\style{font-size:14px}L$ , $\style{font-size:14px}K$ adalah bilangan real dan $\style{font-size:14px}{\;\lim_{x\rightarrow c}\;f(x)\;=\;L}$ , $\style{font-size:14px}{\;\lim_{x\rightarrow c}\;g(x)\;=\;K}$ maka tentukan $begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f squared open parentheses x close parentheses minus L squared over denominator f squared open parentheses x close parentheses plus L squared end fraction end style$ !

S. Nur

Master Teacher

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

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

4.8 (9 rating)

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