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Hitunglah tiap limit fungsi berikut!

Hitunglah tiap limit fungsi berikut!

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Jawaban:

Gunakan akar sekawan untuk mengerjakan soal berikut
Akar sekawan dari begin mathsize 14px style 2 minus square root of x squared plus 3 end root end style adalah begin mathsize 14px style 2 plus square root of italic x squared plus 3 end root end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction cross times fraction numerator 2 plus square root of x squared plus 3 end root over denominator 2 plus square root of x squared plus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis 1 minus x squared right parenthesis left parenthesis 2 plus square root of x squared plus 3 end root right parenthesis over denominator 4 plus 2 square root of x squared plus 3 end root minus 2 square root of x squared plus 3 end root minus left parenthesis x squared plus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis 1 minus x squared right parenthesis left parenthesis 2 plus square root of x squared plus 3 end root right parenthesis over denominator 4 minus left parenthesis x squared plus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses 1 minus x squared close parentheses open parentheses 2 plus square root of x squared plus 3 end root close parentheses over denominator 4 minus x squared minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis 1 minus x squared right parenthesis left parenthesis 2 plus square root of x squared plus 3 end root right parenthesis over denominator 1 minus x squared end fraction end cell row blank equals cell limit as x rightwards arrow 1 of 2 plus square root of x squared plus 3 end root end cell row blank equals cell 2 plus square root of 1 squared plus 3 end root end cell row blank equals cell 2 plus square root of 1 plus 3 end root end cell row blank equals cell 2 plus square root of 4 end cell row blank equals cell 2 plus 2 end cell row blank equals 4 end table end style 

Jadi, diperoleh hasil begin mathsize 14px style lim with italic x yields 1 below fraction numerator 1 minus sign italic x squared over denominator 2 minus sign square root of italic x squared plus 3 end root end fraction equals 4 end style 

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