SOLUTION: If {{{ 2−x^2 }}} ≤ {{{ g(x) }}} ≤ {{{ 2cos(x) }}} for all x, find lim(x→0) {{{ g(x) }}}

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: If {{{ 2−x^2 }}} ≤ {{{ g(x) }}} ≤ {{{ 2cos(x) }}} for all x, find lim(x→0) {{{ g(x) }}}      Log On


   

Question 1013489: If +2%26%238722%3Bx%5E2+ ≤ +g%28x%29+ ≤ +2cos%28x%29+ for all x, find lim(x→0) +g%28x%29+
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Since cos(x) cannot be greater than 1, it appears that for
2 <= g(x) <= 2cos(x)
yields
1 <= (1/2)g(x) <= cos(x)
and cos(x) = (1/2)g(x) = 1
Now cos(0) = 1.
Therefore it appears g(0) = 2.