Ayuda?

1) (la 2 es lo mismo)

<img src="https://tex.z-dn.net/?f=L%3D%5Clim%5Climits_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B2%7D-x%5Cright%29%5Ctan%20x%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx-%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cto%200%7D%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B2%7D-x%5Cright%29%5Ctan%20x%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7B%5Cxi%5Cto%200%7D-%5Cxi%5Ctan%20%5Cleft%28%5Cxi%2B%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7B%5Cxi%5Cto%200%7D%5Cxi%5Ccot%20%5Cxi%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7B%5Cxi%5Cto%200%7D%5Cdfrac%7B%5Cxi%7D%7B%5Ctan%5Cxi%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BL%3D1%7D" />

(3)

<img src="https://tex.z-dn.net/?f=L%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B%5Csqrt%7B1%2B2x%7D-3%7D%7Bx-4%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B%5Csqrt%7B1%2B2x%7D-3%7D%7Bx-4%7D%5Ccdot%20%5Cdfrac%7B%5Csqrt%7B1%2B2x%7D%2B3%7D%7B%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B%5Csqrt%7B1%2B2x%7D%5E2-3%5E2%7D%7B%28x-4%29%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B%281%2B2x%29-9%7D%7B%28x-4%29%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B2x-8%7D%7B%28x-4%29%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B2%28x-4%29%7D%7B%28x-4%29%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%204%7D%5Cdfrac%7B2%7D%7B%5Csqrt%7B1%2B2x%7D%2B3%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BL%3D%5Cdfrac%7B1%7D%7B3%7D%7D" />.