Hawkeye!

Algebra Level 4

f ( x ) = x ( x − 1 ) ( 2 x − 1 ) ( x − 2 ) \large f(x) = \dfrac{ x(x-1)}{(2x-1)(x-2)}

Let the range of the function f ( x ) f(x) above be ( a , b ) (a,b) . Find the value of lim ⁡ y → b 5 y 2 y + 3 y \displaystyle \lim _{y \to b} \frac{5^y}{2^y +3 ^y} . If you think the limit does not exist, submit your answer as 42.


The answer is 42.

Harsh Shrivastava by Harsh Shrivastava , 20, India

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1 solution

To find range of the expression, before jumping onto heavy machinery, first observe that since one of the roots of the expression lies between the asymptotes, the range has to be all reals. If you want a proof, ask in the comments section.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

100% got this right. Amazing :)

Rahil Sehgal - 4 years, 1 month ago

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since u have three attempts,many hazard 42 as their first guess without much thought!!

Rohith M.Athreya - 4 years, 1 month ago

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Ya!! Thats true....😁

Devansh Jain - 4 years, 1 month ago

Nice way to do it by observing how many roots lie between the asymptotes!

Wei Chen - 4 years, 1 month ago

@Harsh Shrivastava Please provide the proof or at least explain the property you have used

ankit agrawal - 4 years, 1 month ago

@Harsh Shrivastava Coincidentally, the answer of the question is the answer to the ultimate question of the life, the universe and everything!!!!

Aaghaz Mahajan - 3 years ago

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