lim x--->0 (sqroot(x+25)-5)/X Solution lim[x?0] (v(x+25) - 5) / x x = 0.1 ---->

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Explanation / Answer

lim[x?0] (v(x+25) - 5) / x x = 0.1 ----> (v(0.1+25)-5)/0.1 = 0.0999002 x = 0.01 ----> (v(0.01+25)-5)/0.01 = 0.099990002 x = 0.001 ----> (v(0.001+25)-5)/0.001 = 0.09999900002 x = -0.1 ----> (v(-0.1+25)-5)/-0.1 = 0.100100201 x = -0.01 ----> (v(-0.01+25)-5)/-0.01 = 0.100010002 x = -0.001 ----> (v(-0.001+25)-5)/-0.001 = 0.10000100002 Limit seems to be approaching 0.1 -------------------- We can calculate exact value of limit as follows: lim[x?0] (v(x+25)-5) / x = lim[x?0] (v(x+25)-5)(v(x+25)+5) / (x(v(x+25)+5)) = lim[x?0] ((x+25)-25) / (x(v(x+25)+5)) = lim[x?0] x/(x(v(x+25)+5)) = lim[x?0] 1/(v(x+25)+5) = 1/(v25+5) = 1/(5+5) = 1/10 = 0.1

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