Jika f(x)=2x−x2 dengan daerah asal D1​={x∣x∈R}. Maka tentukan nilai x→2lim​x2−4f(x)−f(−2)​!

Pertanyaan

Jika begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus x squared end style dengan daerah asal begin mathsize 14px style D subscript 1 equals open curly brackets x vertical line x element of R close curly brackets end style. Maka tentukan nilai begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator f open parentheses x close parentheses minus f open parentheses negative 2 close parentheses over denominator x squared minus 4 end fraction end style!

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator f open parentheses x close parentheses minus f open parentheses negative 2 close parentheses over denominator x squared minus 4 end fraction 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 fraction numerator negative 3 over denominator 2 end fraction end cell end table end style.

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x minus x squared end cell row blank blank cell limit as x rightwards arrow 2 of fraction numerator f open parentheses x close parentheses minus f open parentheses negative 2 close parentheses over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 2 x minus x squared minus open parentheses 2 open parentheses negative 2 close parentheses minus open parentheses negative 2 close parentheses squared close parentheses over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 2 x minus x squared minus open parentheses negative 4 minus 4 close parentheses over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 2 x minus x squared plus 8 over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses negative x minus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses negative x minus 4 close parentheses over denominator open parentheses x plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 minus 4 close parentheses over denominator open parentheses 2 plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 2 end fraction end cell end table end style

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator f open parentheses x close parentheses minus f open parentheses negative 2 close parentheses over denominator x squared minus 4 end fraction 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 fraction numerator negative 3 over denominator 2 end fraction end cell end table end style.

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