Question

For the given function? f(x) and numbers? L,

cc?,

and

epsilon greater than 0?>0?,

find an open interval about

cc

on which the inequality

StartAbsoluteValue f left parenthesis x right parenthesis minus Upper L EndAbsoluteValue less than epsilonf(x)?L<?

holds. Then give a value for

delta greater than 0?>0

such that for all x satisfying

0 less than StartAbsoluteValue x minus c EndAbsoluteValue less than delta0<x?c<?

the inequality

StartAbsoluteValue f left parenthesis x right parenthesis minus Upper L EndAbsoluteValue less than epsilonf(x)?L<?

holds.

?f(x)equals=?mx,

mgreater than>?0,

Lequals=7 m7m?,

ccequals=77?,

epsilon?equals=0.020.02

For what open interval does the inequality

StartAbsoluteValue f left parenthesis x right parenthesis minus Upper L EndAbsoluteValue less than epsilonf(x)?L<?

?hold?

nothing

?(Type your answer in interval? notation.)Find the largest value

delta?greater than>0

such that for all x satisfying

0 less than StartAbsoluteValue x minus c EndAbsoluteValue less than delta0<x?c<?

the inequality

StartAbsoluteValue f left parenthesis x right parenthesis minus Upper L EndAbsoluteValue less than epsilonf(x)?L<?

holds.

delta?equals=nothing