(1) Let . Note that and . Now invoke intermediate-value theorem.
(2)(a) Hint: Given , take
(2)(b) Hint: Does exist?
1.)Show that there is one real number x such that 2cosx = x^2. Justify your answer
2.)Let g(x) = x^(2/5)
a.) is g continuous at x=0? Use the definition of continuity to justify.
b.) is g differentiable at x=0? Use the definition of differentiability to justify.