91Ó°ÊÓ

Find \(\lim _{\mathrm{x}} \rightarrow{ }_{2} \mathrm{f}(\mathrm{x})=2 \mathrm{x}+1\)

Find \(\lim _{\mathrm{x}} \rightarrow{ }_{3} \mathrm{f}(\mathrm{x})=\left[\left(\mathrm{x}^{2}-9\right) /(\mathrm{x}+1)\right]\)

Find \(\lim _{\mathrm{x}} \rightarrow{ }_{2}\left[\left(\mathrm{x}^{2}-5\right) /(\mathrm{x}+3)\right]\)

Find \(\lim _{\mathrm{x}} \rightarrow{ }_{2}\left[(4 \mathrm{x}-3) /\left(\mathrm{x}^{2}+2 \mathrm{x}+5\right)\right]\)

Find \(\lim _{\mathrm{x}} \rightarrow_{3} \mathrm{f}(\mathrm{x})=\left[(1) /(\mathrm{x}-3)^{2},\right] \mathrm{x} \neq\),

Find \(\lim _{\mathrm{x}} \rightarrow{ }_{3}[(5 \mathrm{x}) /(6-2 \mathrm{x})]\)

Find: (a) \(\lim _{\mathrm{x}} \rightarrow 3+\left[\left(\mathrm{x}^{2}+\mathrm{x}+2\right) /\left(\mathrm{x}^{2}-2 \mathrm{x}-3\right)\right]\) (b) \(\lim _{\mathrm{x}} \rightarrow_{3-}\left[\left(\mathrm{x}^{2}+\mathrm{x}+2\right) /\left(\mathrm{x}^{2}-2 \mathrm{x}-3\right)\right]\) (c) \(\lim _{\mathrm{x}} \rightarrow{ }_{3}\left[\left(\mathrm{x}^{2}+\mathrm{x}+2\right) /\left(\mathrm{x}^{2}-2 \mathrm{x}-3\right)\right]\)

Find \(\operatorname{limit}_{\mathrm{x}} \rightarrow{ }_{0}\left[\operatorname{limit}_{\mathrm{y}} \rightarrow_{0}\left\\{\left(\mathrm{ax}^{2}+\mathrm{bxy}+\mathrm{cy}^{2}\right) /\left(\mathrm{d} \mathrm{x}^{2}+\mathrm{exy}+\mathrm{fy}^{2}\right)\right\\}\right]\) \(-\) limit \(_{\mathrm{y}} \rightarrow_{0}\left[\operatorname{limit}_{\mathrm{x}} \rightarrow_{0}\left\\{\left(\mathrm{ax}^{2}+\mathrm{bxy}+\mathrm{cy}^{2}\right) /\left(\mathrm{d} \mathrm{x}^{2}+\mathrm{exy}+\mathrm{fy}^{2}\right)\right\\}\right]\) \(\mathrm{ad} \neq 0, \mathrm{cf} \neq 0\)

Find \(\lim _{(\mathrm{x}, \mathrm{y})} \rightarrow_{(0,0)}\left[\left(\mathrm{x}^{2}-\mathrm{y}^{2}\right) /\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)\right]\)

Given that \(\mathrm{f}\) is the function defined by \(f(x)=x-3 \quad\) if \(x \neq 4\) \(5 \quad\) if \(\mathrm{x}=4\) find \(\lim _{\mathrm{x}} \rightarrow_{4} \mathrm{f}(\mathrm{x})\).