I BELIEVE THEY ALL EXIST. PLEASE FIND EXAMPLES FOR EAXH

Exercise $6\mathrm{.}6\mathrm{.}7.$ Find an example of each of the following or explain why no such function exists.

$($a$)$ An infinitely differentiable function $g(x)$ on all of $R$ with a Taylor series that converges to $g(x)$ only for xin$(-1,1).$

$($b$)$ An infinitely differentiable function $h(x)$ with the same Taylor series as $sinx$ but such that $h(x)sinx$ for all $x0.$

$($c$)$ An infinitely differentiable function $f(x)$ on all of $R$ with a Taylor series that converges to $f(x)$ if and only if $x0.$