Quick basic calculus question

[Wahamuka]

What did I do wrong here? The answer is suppose to be 2 but I got -2

Ignore the red pen marking thats wrong

 

[Harry_the_cat]

First of all, before I look closer, can you please check that the sign in the middle of the original question is, in fact, a minus sign and not a plus sign?

 

[Harry_the_cat]

OK, the sign in the middle is correct.

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.

 

[Wahamuka]

No we haven’t learned l'hopital's rule. I’ll read up on it thanks! I never would have thought about that

 

[Harry_the_cat]

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

 

[Wahamuka]

Which part of the solution do i apply l'hopital's rule?

 

[Harry_the_cat]

The first term. The second term is separate and you've done that correctly.

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.

 

[Harry_the_cat]

Did you get it?

 

[Wahamuka]

Just got it now. I skipped this question first because although this is in our worksheet, we haven't even studied derivatives so I doubt this will appear in my test on Monday. But I get it, its just that chain rule is weird for me because we haven't discussed it yet.

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

 

[Dr.Peterson]

You don't need L'Hopital. Did you consider multiplying by the conjugate of the denominator? (I'd do that before squaring.)

 

[Harry_the_cat]

Just got it now. I skipped this question first because although this is in our worksheet, we haven't even studied derivatives so I doubt this will appear in my test on Monday. But I get it, its just that chain rule is weird for me because we haven't discussed it yet.

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

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

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

 

[Wahamuka]

You don't need L'Hopital. Did you consider multiplying by the conjugate of the denominator? (I'd do that before squaring.)

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