lim (x tends to 0) [{root(x^2+1) -1}]/[{root(x^2+9) -3}] = ?

Dear Student,
Please find below the solution to the asked query:

limx0x2+1-1x2+9-3=limx0x2+1-1x2+9-3×x2+9+3x2+9+3=limx0x2+1-1x2+9+3x2+9-9=limx0x2+1-1x2+9+3x2×x2+1+1x2+1+1=limx0x2+1-1x2+9+3x2x2+1+1=limx0x2x2+9+3x2x2+1+1=limx0x2+9+3x2+1+1=0+9+30+1+1=3+31+1=62=3

Regards

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