Teaching EMRS PGT Mock Test 2023 Mathematics Limit and Continuity

If \(\displaystyle\lim_{x\rightarrow\infty}\left(\dfrac{x^2+5}{2x+3}-ax-b\right)=\infty\), then the value of a and b are:

1
\(a=\dfrac{1}{2}\), b ∉ ℝ
2
\(a\ne\dfrac{1}{2}\), b ∈ ℝ
3
\(a=\dfrac{1}{2}\), b ∈ ℝ
4
\(a\ne\dfrac{1}{2}\), b ∉ ℝ
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