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lim(x->(pi/4)) (sqrt(2) cosx-1)/(cot x-1...

`lim_(x->(pi/4)) (sqrt(2) cosx-1)/(cot x-1)`

Text Solution

Verified by Experts

`cos x -> 1/sqrt2 `
`cot x -> 1`
`lim_(x-> pi/4) (d/dx(sqrt2 cos x - 1))/(d/dx(cot x - 1))`
`lim_(x->pi/4) ( sqrt2 (-sinx))/(cosec^2 x)`
`= (sqrt2 xx -1/sqrt2)/-(sqrt2)^2`
`= -1/-2 = 1/2`
Answer
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