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Tentukan! b.

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Tentukan!

b. begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction end style 

Pembahasan Soal:

Bentuk begin mathsize 14px style limit as x rightwards arrow a of f open parentheses x close parentheses comma space a not equal to 0 end style dan begin mathsize 14px style f open parentheses x close parentheses end style merupakan fungsi rasional (pecahan), lakukan tes limit dengan substitusi nilai begin mathsize 14px style x equals a end style ke fungsi undefined, jika diperoleh hasil begin mathsize 14px style 0 over 0 end style, lakukan faktorisasi undefined atas faktor linearnya sehingga penyebab bentuk begin mathsize 14px style 0 over 0 end style, dapat dihilangkan.

Tes limit dengan substitusi nilai begin mathsize 14px style x equals a end style ke fungsi undefined, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction end cell equals cell fraction numerator open parentheses 3 close parentheses squared minus 5 open parentheses 3 close parentheses plus 6 over denominator open parentheses 3 close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator 9 minus 15 plus 6 over denominator 3 minus 3 end fraction end cell row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction end cell equals cell 0 over 0 end cell end table end style 

Diperoleh hasil begin mathsize 14px style 0 over 0 end style, sehingga dilakukan faktorisasi undefined, perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 2 close parentheses open parentheses x minus 3 close parentheses over denominator open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses x minus 2 close parentheses end cell row blank equals cell 3 minus 2 end cell row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction end cell equals 1 end table end style 

Jadi, diperoleh begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator x minus 3 end fraction equals 1 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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