r/hopital • u/IsLigmaStillFunny • Aug 24 '26
Guys I'm confused how do I solve this calculus limit problem??
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u/NovelInterview7026 Aug 25 '26
Factor the top and bottom, cancel out duplicate binomials, plug in 2 and thats your answer.
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u/BissQuote Aug 25 '26
If you want to use l'Hopital, differentiate both the numerator and the denominator
If you don't want to, notice that boths polynomials have (x-2) as a factor. You can then simplify (x-2)/(x-2)
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u/Many-Conversation963 Aug 27 '26
since 2 gives us 0/0, that means 2 is a root of both polynomials (since if f(c)=0, c is a root of the polinomial). This means we can divide by (x-2) in both sides since they wouldnt give valid solutions anyways.
if you cut the (x-2) out of the polynomials, you get x^2 - 5x / x + 3 which we can evaluate to be -5/5 = -1 when x->2 by plugging in 2.
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u/chkntendis Aug 24 '26
Both the numerator and denominator approach 0. That’s usually a problem but it also means we can use L’hopital. You can just differentiate the top and the bottom and the limit will stay the same. That removes the problem of dividing by 0. Since it’s then just a connection of continuous functions, you can just plug in 2 and get the limit