- #1
kingstrick
- 108
- 0
Want to show that f(x)/g(x) is continuous as x goes to c given that g(c) is not 0 and f(c) exists.
|f(x)/g(x) - f(c)/g(c)| = |1/(g(x)g(c))||f(x)g(c)-f(c)g(x)| = |1/(g(x)g(c))||f(x)g(c)-f(c)g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g(c))|||f(x)||g(x)-g(c)| + |g(x)||f(x)- f(c)||
Now I am stuck
|f(x)/g(x) - f(c)/g(c)| = |1/(g(x)g(c))||f(x)g(c)-f(c)g(x)| = |1/(g(x)g(c))||f(x)g(c)-f(c)g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g(c))|||f(x)||g(x)-g(c)| + |g(x)||f(x)- f(c)||
Now I am stuck