Pertanyaan

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

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

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai .

nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px c below fraction numerator size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 2 over denominator size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px minus size 14px 2 end fraction size 14px equals fraction numerator size 14px L size 14px plus size 14px 2 over denominator size 14px L size 14px minus size 14px 2 end fraction$ .

Pembahasan

Catatan: Pada soal seharusnya yang ditanyakan adalah . Sifat yang digunakan: 1. 2. 3. Dapat diperoleh Jadi, nilai .

Catatan:

Pada soal seharusnya yang ditanyakan adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow c of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator f left parenthesis x right parenthesis plus 2 over denominator f left parenthesis x right parenthesis minus 2 end fraction end cell end table end style$ .

Sifat yang digunakan:

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

Dapat diperoleh

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

Jadi, nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px c below fraction numerator size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 2 over denominator size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px minus size 14px 2 end fraction size 14px equals fraction numerator size 14px L size 14px plus size 14px 2 over denominator size 14px L size 14px minus size 14px 2 end fraction$ .