- Thread starter Wahamuka
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The limit of the last term is 2 so that half is correct.

With the first term, the red is, in fact, correct. In black, you had expanded the square of the difference incorrectly.

So following the red working through you still end with 0/0 when you sub in x=0. Have you learnt l'hopital's rule? If you apply this twice to the corrected version you get 4 for the first half of the limit. You can verify this by using graphing software.

So 4 - 2 gives you 2.

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l'hopital's rule is pretty easy to apply. It involves differentiation.

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So let \(\displaystyle f(x)= x^2\) and \(\displaystyle g(x) =2 + x - 2\sqrt{x+1}\)

Notice that f(0) = 0 and g(0)=0. This is your cue that applying l'hopital's rule may help.

You will have to do the process a second time. Let me know how you go.

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Did you get it?

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Thanks! I’d be stuck in this problem till now if you hadn’t introduced “that” concept, idk why my teacher gave this

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OK if you haven't studied derivatives yet then you wouldn't be expected to do it that way.

Thanks! I’d be stuck in this problem till now if you hadn’t introduced “that” concept, idk why my teacher gave this

Try what Dr P said in post #10. No derivatives involved.

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Thats very shocking! Now it makes sense why it was on the worksheet! Thank you so much ;w; I’ll now remember to simplify the insides first