If Lim x → ∞ x ( tan − 1 ( x + μ x + λ ) − 4 π ) = 1 then ordered pair(s) ( λ , μ ) can be

Question

If Lim x → ∞ ​ x ( tan − 1 ( x + μ x + λ ​ ) − 4 π ​ ) = 1 then ordered pair(s) ( λ , μ ) can be

TestHub · Accepted Answer

x → ki L im ​ x 1 ​ tan − 1 ( x + μ x + λ ​ ) − 4 π ​ ​ = 1 Apply L' hospital rule and simplifying we get x → ∞ L im ​ 2 x 2 + 2 x ( λ + μ ) + ( μ 2 + λ 2 ) ( λ − μ ) x 2 ​ = 1 \eqalign{ & \Rightarrow \,\,\,\,{{\lambda - \mu } \over 2} = 1 \cr & \Rightarrow \,\,\,\lambda - \mu = 2 \cr} ( λ , μ ) can be (5, 3)

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