Prove statement 6 of theorem A f(x) g(x) 1 M f(x) g(x) Lg(x) Lg(x) LM g(X) f(x) L L g(x) M curren g(x) f(x) L L g(X) M Now show that if Then there is a number Icirc acute 1 such that 0 lim g(x)M

Question: Prove statement 6 of theorem A. |f(x) g(x) - 1.M = |f(x) g(x) - Lg(x) + Lg(x) - LM| = |g(X) [f(x) - L] +

Prove statement 6 of theorem A.
|f(x) g(x) - 1.M = |f(x) g(x) - Lg(x) + Lg(x) - LM|
= |g(X) [f(x) - L] + L[g(x) - M]|
‰¤ |g(x) ||f(x) - L| + |L|| g(X) - M|
Now show that if

Then there is a number Î´1 such that
0

lim g(x)M

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