# ppprove or desprove question

• September 6th 2011, 10:24 AM
transgalactic
ppprove or desprove question
prove or display a desproving example:
A)
there is f and g which are defined $x_{0}-\delta for which $lim_{x->x_{0}}f(x)g(x)=\infty$.
if 0<g(x)<1 for $x\in N_{\delta}^{*}(x_{0})$ then $lim_{x->x_{0}}f(x)=\infty$
B)
if f monotonickly decreasing in $[0,\infty)$ and $lim_{x->\infty}f(x)=0$ then f(x)>0 for all $x\in[0,\infty)$
C)if f differentiable in (a,b) so $lim_{x->a^{+}}f(x)=lim_{x->b^{-}}f(x)=1$ then there is $c\in(a,b)$ so $f'(c)=0$
D)if f is integrabile in [a,b] then there is x in [a,b] so $\int_{a}^{x}f(t)dt=\int_{x}^{b}f(t)dt$

regarding a:
i dont know from the start how to know intuetivly whether its true or false
?