Question

Show by means of an example that
lim x-> a [f(x) + g(x)] may exist evn though neither lim x-> a f(x) adn lim x -> a g(x) exists.

Answer 1

Sure. Take a = 0. What's a function that doesn't have a limit there?

One such function is f(x) = 1/x. Another is g(x) = x - 1/x.

But f(x) + g(x) = x does have a limit at 0.

Answer 2

\[f(x)=\left\{\begin{matrix}1, & x\ge 0, \\ 0 & x<0\end{matrix}\right.\]

\[g(x)=\left\{\begin{matrix}0, & x\ge 0, \\ 1 & x<0\end{matrix}\right.\]

Answer 3

is taht the answer? the two values of f(x) and g(x)

Answer 4

also Show by means of an example that
lim x-> a [f(x)g(x)] may exist evn though neither lim x-> a f(x) adn lim x -> a g(x) exists.

Answer 5

I guess I should write

\[f(x)=\left\{\begin{matrix}1, & x\ge a \\ 0, & x<a\end{matrix}\right.\]

\[g(x)=\left\{\begin{matrix}0, & x\ge a \\ 1, & x<a\end{matrix}\right.\]

Answer 6

you can use my f,g for both questions

Answer 7

f+g=1
f*g=0

but neither limit exists on its own

Answer 8

i see...but y is taht it doesnt exist on its own

Answer 9

limit from one side is 1 and from the other side is 0...they are different so the limit does not exist

Answer 10

ohhh i always forget taht if teh RHL and teh LHL do not match it does not exist

Answer 11

can u help me w/ a dfft limit problem

Answer 12

i dont understand it

Answer 13

add a new post. I'm sure someone will help you

Answer 14

ok