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Tentukan nilai limit fungsi berikut. 6. x → 7 lim ​ x 2 − 10 x + 21 2 x 2 − 8 x − 42 ​

Tentukan nilai limit fungsi berikut.

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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nilai dari .

nilai dari begin mathsize 14px style limit as x rightwards arrow 7 of space fraction numerator 2 x squared minus 8 x minus 42 over denominator x squared minus 10 x plus 21 end fraction equals 5 end style.

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Pembahasan

Diketahui: Pembagian limit fungsi. Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut: Substitusi dengan pada limit fungsi yang telah disederhanakan seperti berikut: Jadi, nilai dari .

Diketahui:

Pembagian limit fungsi.

Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 7 of space fraction numerator 2 x squared minus 8 x minus 42 over denominator x squared minus 10 x plus 21 end fraction end cell equals cell limit as x rightwards arrow 7 of space fraction numerator 2 open parentheses x squared minus 4 x minus 21 close parentheses over denominator x squared minus 3 x minus 7 x plus 21 end fraction end cell row blank equals cell limit as x rightwards arrow 7 of space fraction numerator 2 open parentheses x squared plus 3 x minus 7 x minus 21 close parentheses over denominator x open parentheses x minus 3 close parentheses minus 7 open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 7 of space fraction numerator 2 open parentheses x open parentheses x plus 3 close parentheses minus 7 open parentheses x plus 3 close parentheses close parentheses over denominator open parentheses x minus 7 close parentheses open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 7 of space fraction numerator 2 down diagonal strike open parentheses x minus 7 close parentheses end strike open parentheses x plus 3 close parentheses over denominator down diagonal strike open parentheses x minus 7 close parentheses end strike open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 7 of space fraction numerator 2 open parentheses x plus 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 7 of space fraction numerator 2 x plus 6 over denominator x minus 3 end fraction end cell end table end style

Substitusi begin mathsize 14px style x end style dengan begin mathsize 14px style 7 end style pada limit fungsi yang telah disederhanakan seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 7 of space fraction numerator 2 x plus 6 over denominator x minus 3 end fraction end cell equals cell fraction numerator 2 open parentheses 7 close parentheses plus 6 over denominator 7 minus 3 end fraction end cell row blank equals cell fraction numerator 14 plus 6 over denominator 4 end fraction end cell row blank equals cell 20 over 4 end cell row blank equals 5 row blank blank blank end table end style

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 7 of space fraction numerator 2 x squared minus 8 x minus 42 over denominator x squared minus 10 x plus 21 end fraction equals 5 end style.

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