Eavaluate each linit analytically without using L'Hospital's Rule. Show work

$\underset{x5}{lim}\frac{x^2-3x-10}{x-5}$

$\underset{x-1}{lim}\frac{\sqrt[\phantom{2}]{2x+3}-1}{x+1}$

$\underset{x0}{lim}\frac{2sinxcosx}{x}$

$\underset{x\frac{5}{3}}{lim}\frac{5-3x}{9x^2-25}$

$\underset{\frac{}{4}}{lim}(4sin-2cos)$