91Ó°ÊÓ

Find equations for these lines: a. Passes through the points \((-1,3)\) and \((4,1)\). b. \(x\) intercept \((3,0)\) and \(y\) intercept \(\left(0,-\frac{2}{3}\right)\) c. Contains \((-1,3)\) and is perpendicular to \(5 x-3 y=7\)

Find the points of intersection (if any) of the given pair of curves, and draw the graphs. a. \(y=-3 x+5\) and \(y=2 x-10\) b. \(y=x+7\) and \(y=-2+x\)

Find \(c\) so that the curve \(y=3 x^{2}-2 x+c\) passes through the point \((2,4)\).

Find \(c\) so that the curve \(y=4-x-c x^{2}\) passes through the point \((-2,1)\).

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 1} \frac{x^{2}+x-2}{x^{2}-1} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 2} \frac{x^{2}-3 x}{x+1} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 2} \frac{x-8}{2-x} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 1}\left(\frac{1}{x^{2}}-\frac{1}{x}\right) $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty}\left(2+\frac{1}{x^{2}}\right) $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty} \frac{x}{x^{2}+5} $$