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Hitunglah limit fungsi berikut.

Hitunglah limit fungsi berikut.

begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator square root of x minus square root of 5 over denominator open parentheses x minus 5 close parentheses left parenthesis square root of x plus square root of 5 right parenthesis end fraction end style  undefined 

  1. ... undefined 

  2. ... undefined 

Jawaban:

Dalam hal ini undefined dimanipulasi dengan cara mengalikan akar sekawan, akar sekawan dari undefined adalah undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of fraction numerator square root of x minus square root of 5 over denominator open parentheses x minus 5 close parentheses open parentheses square root of x plus square root of 5 close parentheses end fraction end cell equals cell limit as x rightwards arrow 5 of fraction numerator square root of x minus square root of 5 over denominator open parentheses x minus 5 close parentheses open parentheses square root of x plus square root of 5 close parentheses end fraction cross times fraction numerator square root of x plus square root of 5 over denominator square root of x plus square root of 5 end fraction end cell row blank equals cell limit as x rightwards arrow 5 of fraction numerator x minus 5 over denominator open parentheses x minus 5 close parentheses open parentheses square root of x plus square root of 5 close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow 5 of 1 over open parentheses square root of x plus square root of 5 close parentheses squared end cell row blank equals cell 1 over open parentheses square root of 5 plus square root of 5 close parentheses squared end cell row blank equals cell 1 over open parentheses 2 square root of 5 close parentheses squared end cell row blank equals cell 1 over 20 end cell end table end style

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator square root of x minus square root of 5 over denominator open parentheses x minus 5 close parentheses open parentheses square root of x plus square root of 5 close parentheses end fraction equals 1 over 20 end style

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