Question

Limθ→π/4 (cosθ−sinθ​)/(θ– π/4)​

Answer 1

-√2

Explanation:

For the typing purpose I replaced θ with n in the calculation

`\lim_{n \to (\pi )/(4)} (cos n-sin n)/((\pi )/(4) ) ...limits L'Hopital's Rule\\= \lim_{n \to (\pi )/(4)} (-sin n-cos n)/(1 ) ... plug. in . (\pi )/(4) \\= - sin (\pi )/(4) - cos (\pi )/(4)\\= - (√(2) )/(2) - (√(2) )/(2)\\= (- 2√(2))/(2) \\= - √(2)`