Lim x->c[f(x)+g(x)]: Examples to Show No Implication

[ussjt]

Can someone point me in the right dirrection with this problem:

find examples to show that if

a) lim x->c [f(x)+g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

b) lim x->c [f(x)*g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

any help would be great

 

[HallsofIvy]

Think simply: if f(x)= 1/x, what is the limit as x-> 0? what is limit of g(x)= -1/x as x-> 0? What about f(x)+ g(x)?

 

[ussjt]

would that still work for part B of the problem?

 

[Jameson]

Not that example because there is no limit of f(x)*g(x). Use the two examples of x^2 and 1/x^2