The value of \lim_{x \to \infty} {x^{2}-5 x+4}/{4 x^{2}+2 x} is

GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 13 of 65

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The value of

\lim ↙{x → ∞} \;{x^{2}-5 x+4}/{4 x^{2}+2 x}

Solution:

\lim ↙{x → 0} \;{x^{2}-5 x+4}/{4 x^{2}+2 x}=\;{4}/{0}=0

Applying L's Hospital rule

\lim ↙{x → 0} \;{f^{1}(x)}/{f^{1}(x)}=\;{2 x-5}/{8 x+2}=-v e

So again applying L's Hospital rule

\lim ↙{x → 0} f^{' '}(x)=\;{2}/{8}=\;{1}/{4}

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