lim x -> 0

Please help ASAP. Thanks!

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1 Answer

Best answer

x+25 can be written 25+x=25(1+x/25), so √(x+25)=√(25(1+x/25))=5√(1+x/25).

When x is small, √(1+x/25)=(1+x/25)^½≈1+x/50, so the whole expression becomes (5(1+x/50)-5)/x=(5+x/10-5)/x=1/10.

Therefore the limit is 1/10.

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