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Hitunglah limit fungsi berikut!

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

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nilai  size 14px lim with size 14px h size 14px rightwards arrow size 14px 0 below fraction numerator square root of size 14px x size 14px plus size 14px h end root size 14px minus square root of size 14px x over denominator size 14px h end fraction adalah fraction numerator 1 over denominator 2 x end fraction square root of x . 

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begin mathsize 14px style h equals 0 end style disubtitusikan pada limit tersebut

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

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan mengalikan akar sekawan

      space space space space space limit as h rightwards arrow 0 of fraction numerator square root of x plus h end root minus square root of x over denominator h end fraction times fraction numerator square root of x plus h end root plus square root of x over denominator square root of x plus h end root plus square root of x end fraction left right double arrow limit as h rightwards arrow 0 of fraction numerator open parentheses x plus h close parentheses minus x over denominator h open parentheses square root of x plus h end root minus square root of x close parentheses end fraction left right double arrow limit as h rightwards arrow 0 of fraction numerator h over denominator h open parentheses square root of x plus h end root minus square root of x close parentheses end fraction left right double arrow fraction numerator 1 over denominator open parentheses square root of x plus 0 end root minus square root of x close parentheses end fraction left right double arrow fraction numerator 1 over denominator 2 square root of x end fraction equals fraction numerator 1 over denominator 2 x end fraction square root of x

Jadi, nilai  size 14px lim with size 14px h size 14px rightwards arrow size 14px 0 below fraction numerator square root of size 14px x size 14px plus size 14px h end root size 14px minus square root of size 14px x over denominator size 14px h end fraction adalah fraction numerator 1 over denominator 2 x end fraction square root of x . 

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