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Hitunglah setiap limit berikut ini!

Hitunglah setiap limit berikut ini!

 begin mathsize 14px style 4. space limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus 1 end fraction end style 

Jawaban:

Kita cek terlebih dahulu apakah hasil limitnya tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style :

1. Jika tidak menghasilkan tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style, maka nilai tersebut adalah nilai limitnya

2. Jika ya menghasilkan tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style, maka selesaikan dengan metode mengalikan akar sekawan

Cek :

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus 1 end fraction equals fraction numerator 0 over denominator square root of 1 plus 0 end root minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 0 over denominator square root of 1 minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 0 over 0 end style

Karena menghasilkan bentuk tak tentu, maka selesaikan dengan metode mengalikan akar sekawan.

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

jadi, begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus 1 end fraction equals 2 end style

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