If lim x → 1 + ( x − 1 ) 3 ( x − 1 ) ( 6 + λ c o s ( x − 1 )) + μ s i n ( 1 − x ) = − 1 , where λ , μ ∈ R , then λ + μ is equal to

Question

If lim x → 1 + ​ ( x − 1 ) 3 ( x − 1 ) ( 6 + λ c o s ( x − 1 )) + μ s i n ( 1 − x ) ​ = − 1 , where λ , μ ∈ R , then λ + μ is equal to

TestHub · Accepted Answer

​ Put x = 1 + h h → 0 lim ​ h 3 h ( 6 + λ cosh ) − μ sinh ​ = − 1 h → 0 lim ​ h 3 h ( 6 + λ ( 1 − 2 ! h 2 ​ ) ) − μ ( h − 3 ! h 3 ​ ) ​ = − 1 6 + λ − μ = 0 and − 2 λ ​ + 6 μ ​ = − 1 λ + μ = 18 ​

Mathematics - Limits Question with Solution | TestHub

Options:

Doubts & Discussion