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Calculus and Beyond Homework Help
How to evaluate a limit with roots
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[QUOTE="Simon Bridge, post: 4518456, member: 367532"] If you are used to this sort of stuff it can be shown in about three steps from here. That would make it just-about "doing the problem for him" - I realize. If you are just learning - though - there will still be a bunch of false starts, like we've seen already, and it can get confusing keeping track of all the exponents and where the minus signs go. Making sure students do an exercise like this is supposed to motivate the shortcut approaches. I think MathewsMD has got there already :) The RH parentheses is basically what those a's and b's expand out to and it's the lynchpin. Comparing that with what he got should expose what went wrong. Building on the power rule for integers, already proved by the definition, and using implicit differentiation, turns this into a bunch of much easier steps... and is more like how math is actually done. [/QUOTE]
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How to evaluate a limit with roots
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