Find the limit as theta approaches p/4

Question

lim        cosθ-(1/√2)/(θ-π/4)

θ→π/4

 

I rewrote θ as h so I have lim   which is cosh-(1/√2)/h-(π/4)

                                      h→0

I also know that the lim as h→0 of cosh-1/h is 0 and I would like to get it in that form, but I don't know how to proceed from here to find the limit. 

 

By the way, the correct answer is -1/√2 but I don't know how they came to that conclusion. 

Answer 1

If you evaluate the expression for π/4 you will get 0/0 which is indeterminant.

 

 

You could use L'Hopital's rule by taking the derivatives of the numerator and the denominator and retaking the limit.

 

 

  lim -sin(θ)/1 = -1/√2

θ→π/4