Evaluate \(\lim_{x\to3}(2x+5)\).

If \(\lim_{x\to a}f(x)=4\) and \(\lim_{x\to a}g(x)=-2\), find \(\lim_{x\to a}(3f(x)-g(x))\).

Evaluate \(\lim_{x\to2}(x^2+3x-1)\).

Evaluate \(\lim_{x\to1}\frac{x^2+2}{x+3}\).

Evaluate \(\lim_{x\to4}\frac{x^2-16}{x-4}\).

Evaluate \(\lim_{x\to0}\frac{(x+1)^2-1}{x}\).

Evaluate \(\lim_{x\to9}\frac{\sqrt{x}-3}{x-9}\).

Evaluate \(\lim_{x\to-1}\frac{x^2+3x+2}{x+1}\).

Given \(\lim_{x\to2}f(x)=5\) and \(\lim_{x\to2}g(x)=0\), explain why the quotient law alone does not evaluate \(\lim_{x\to2}\frac{f(x)}{g(x)}\).

Evaluate \(\lim_{x\to0}\frac{\sqrt{4+x}-2}{x}\).