Evaluate: limθ→π4cos⁡θ−sin⁡θθ−π4 My Attempt: This limit takes 00 form when θ=π4. Here, 00 form is an indeterminate form. So how do I make it determinate?

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nghodlokl · Accepted Answer

Without lHospital:

vicki331g8 · Accepted Answer

Since your limit is in the form 00, you can use LHopitals rule.  limθ→π4cos⁡θ−sin⁡θθ−π4=limθ→π4ddθ(cos⁡θ−sin⁡θ)ddθ(θ−π4)=limθ→π4(−sin⁡θ−cos⁡θ)=…  Now that your limit is not indeterminate, you can evaluate your limit by substitution.

nick1337 · Accepted Answer

If you know that for small x you have sin⁡x≈x (from Taylor expansion or l&#039;Hopital), you can write θ−π4=x. Then you can show cos⁡(x+π4)−sin⁡(x+π4)=−2sin⁡x Then your limit is −2

Evaluate: limθ→π4cos⁡θ−sin⁡θθ−π4 My Attempt: This limit takes 00 form when θ=π4. Here, 00 form is...

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