91Ó°ÊÓ

Use factorization to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part \((b)\). (a) \(\frac{x^{3}+3 x^{2}+3 x+1}{x^{4}+x^{3}+x+1}\) (b) \(\lim _{x \rightarrow-1} \frac{x^{3}+3 x^{2}+3 x+1}{x^{4}+x^{3}+x+1}\)

Determine the quadrant in which the given point lies if \((a, b)\) is in quadrant \(I\). $$ (a, a) $$

Complete the square in \(x\) and \(y\) to find the center and the radius of the given circle. \(x^{2}+y^{2}+3 x-16 y+63=0\)

Write the given inequality using interval notation and then graph the interval. $$ -5

Use factorization to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part \((b)\). (a) \(\frac{x^{4}-5 x^{3}+4 x-20}{x^{4}-5 x^{3}+x-5}\) (b) \(\lim _{x \rightarrow 5} \frac{x^{4}-5 x^{3}+4 x-20}{x^{4}-5 x^{3}+x-5}\)

Determine the quadrant in which the given point lies if \((a, b)\) is in quadrant \(I\). $$ (b,-b) $$

Write the given expression without the absolute value symbols. $$ \frac{|x-y|}{|y-x|}, x \neq y $$

Write the expression \(|x-2|+\mid x-\) \(5 \mid\) without the absolute value symbols if the number \(x\) is in the given interval. $$ (-\infty, 1) $$

Complete the square in \(x\) and \(y\) to find the center and the radius of the given circle. \(2 x^{2}+2 y^{2}+4 x+16 y+1=0\)

In Problems \(13-20\), use binomial expansion to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part (b). (a) \(\frac{(2+h)^{2}-4}{h}\) (b) \(\lim _{h \rightarrow 0} \frac{(2+h)^{2}-4}{h}\)