Question

if f and g are continuous at a, prove f-g is continuous at a

Answer 1

is it f minus g?

Answer 2

?

Answer 3

atleast reply only then i will be able to solve...........@bueno

Answer 4

sorry about that, yes it is

Answer 5

if both functions are continuous that means they have defined limits at any point
use properties of limits to prove that the difference f - g also has a defined limit

Answer 6

im really out of practice with limits

Answer 7

could you give me a link to a simple but thurough explanation? im writing on this tomorrow and still have to do curve sketching

Answer 8

sorry openstudy is glitchy

i was saying if you know that

\[\lim_{x \rightarrow c} f(x) = L\]

and

\[\lim_{x \rightarrow c} g(x) = M\]

maybe use the property of limits:

\[\lim_{x \rightarrow c} ( f(x) + g(x) ) = \lim_{x \rightarrow c} f(x) + \lim_{x \rightarrow c} g(x)\]

Answer 9

to show that there is a defined limit on every point of f(x) - g(x)

Answer 10

i meant of limits as x->infinity and the limit laws

Answer 11

maybe i dont understand the question :( what are you trying to prove exactly

Answer 12

i asked instead if you could give me a link to a simple yet thorough explanation of limit laws and limts as x->infinity

Answer 13

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx

Answer 14

thanks!