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Kerjakan pertanyaan berikut dengan benar dan teliti! x→7lim​ x2−492−x−3​​

Pertanyaan

Kerjakan pertanyaan berikut dengan benar dan teliti!

begin mathsize 14px style limit as x rightwards arrow 7 of space fraction numerator 2 minus square root of x minus 3 end root over denominator x squared minus 49 end fraction end style 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style limit as x rightwards arrow 7 of space fraction numerator 2 minus square root of x minus 3 end root over denominator x squared minus 49 end fraction end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px 1 over size 14px 56 end cell end table.

Pembahasan

Dengan menerapkan penyelesaian limit dengan metode mengalikan akar sekawan dan metode pemfaktoran, diperoleh perhitungan sebagai berikut.

limit as x rightwards arrow 7 of space fraction numerator 2 minus square root of x minus 3 end root over denominator x squared minus 49 end fraction equals limit as x rightwards arrow 7 of space fraction numerator 2 minus square root of x minus 3 end root over denominator x squared minus 49 end fraction cross times fraction numerator 2 plus square root of x minus 3 end root over denominator 2 plus square root of x minus 3 end root end fraction equals limit as x rightwards arrow 7 of space fraction numerator 4 minus open parentheses x minus 3 close parentheses over denominator open parentheses x squared minus 49 close parentheses open parentheses 2 plus square root of x minus 3 end root close parentheses end fraction equals limit as x rightwards arrow 7 of space fraction numerator negative x plus 7 over denominator open parentheses x squared minus 49 close parentheses open parentheses 2 plus square root of x minus 3 end root close parentheses end fraction equals limit as x rightwards arrow 7 of space fraction numerator negative up diagonal strike open parentheses x minus 7 close parentheses end strike over denominator up diagonal strike open parentheses x minus 7 close parentheses end strike open parentheses x plus 7 close parentheses open parentheses 2 plus square root of x minus 3 end root close parentheses end fraction equals limit as x rightwards arrow 7 of space fraction numerator negative 1 over denominator open parentheses x plus 7 close parentheses open parentheses 2 plus square root of x minus 3 end root close parentheses end fraction equals fraction numerator negative 1 over denominator open parentheses 7 plus 7 close parentheses open parentheses 2 plus square root of 7 minus 3 end root close parentheses end fraction equals fraction numerator negative 1 over denominator open parentheses 14 close parentheses open parentheses 4 close parentheses end fraction equals negative 1 over 56 

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 7 of space fraction numerator 2 minus square root of x minus 3 end root over denominator x squared minus 49 end fraction end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px 1 over size 14px 56 end cell end table.

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