Find a pair of functions such that the following are true

[Torshi]

Homework Statement

Find a pair of functions f(x), g(x) such that the following are true

lim x->3+ f(x) = +∞
lim x->3+ g(x) = +∞
lim x->3+ (f(x)-g(x)) ≠0

Homework Equations

none

The Attempt at a Solution

f(x) = x/x-3
g(x) 3/x-3
?

 

[SammyS]

Homework Statement

Find a pair of functions f(x), g(x) such that the following are true

lim x->3+ f(x) = +∞
lim x->3+ g(x) = +∞
lim x->3+ (f(x)-g(x)) ≠0

Homework Equations

none

The Attempt at a Solution

f(x) = x/(x-3)
g(x) 3/(x-3)
?

Correct use of parentheses is important .

Well, what is lim x_→3⁺ (f(x)-g(x)) for those functions?

 

[Torshi]

Lim x->3+ (x-3)/(x-3) = 1? ≠0

 

[SammyS]

Lim x->3+ (x-3)/(x-3) = 1? ≠0

Therefore, your choices for f(x) and g(x) look good !

 

[Torshi]

Therefore, your choices for f(x) and g(x) look good !

Thanks!