For the given function f(x) and numbers L, c, and ϵ>0, find an open interval about c on which the inequality |f(x−L|<ϵ holds. Then give a value for δ >0 such that for all x satisfying 0<|x−c|<δ the inequality |f(x)−L|<ϵ holds. f(x)=mx+b, m>0,L=m2+b, c=12,ϵ=k>0.For what open interval does the inequality |f(x)−L|>ϵ hold? (type your answer in interval notation.)
Find the largest value δ>0 such that for all x satisfying 0<|x−c|<δ the inequality |f(x)−L|<ϵ holds.
δ =

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.

146

step-by-step explanation: