Exercise. Consider the function

g

with unknown parameter

b

given below.\

g(x)={((2x+b)/(x-5) if x=0 and x!=4):}

\ The value of

b

such that

g

is continuous at

x=0

is

b=5

\ Exercise.\ Evaluate the limits.\

\\\\lim_(x->-\\\\infty )g(x)=2\ \\\\lim_(x->\\\\infty )g(x)=

\ Exercise.\

g

has a horizontal asymptotes (from bottom to top)

y=0,

and

y=2

\ Exercise.\ Select all vertical asymptotes of

g

below.\

y=\\\\infty \ y=-\\\\infty

\

y=-4

\

x=-16\ y=-16

Exercise. Consider the function g with unknown parameter b given below. g(x)={x52x+bx216x+16ifx