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Evaluate the following limit: lim(x->pi/...

Evaluate the following limit: `lim_(x->pi/4)(sqrt(2)-cos x-sin x)/((pi/4-x)^2)`

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Verified by Experts

`lim_(x->pi/4)(sqrt(2)-cos x-sin x)/((pi/4-x)^2)`
This is `(0/0)` form
So apply L-Hospital Rule
`lim_(x->pi/4)(d/(dx)(sqrt(2)-cos x-sin x))/(d/(dx)((pi/4-x)^2))`
`lim_(x->pi/4) (sin x-cosx)/(2(pi/4-x))`
`lim_(x->pi/4) (cos x+ sinx)/(-2)`
`=(1/(sqrt2)+1/(sqrt2))/(-2)`
`=-1/(sqrt2)`
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