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If f(x) = f(y) for every bounded linear functional f on a normed space X, show that x = y.
Let X be a normed space and X' its dual space. If X¢{O}, show that X' cannot be {O}.
show that if the endpoints of the circle in the above problem lie on the x-axis then the circular Arc must have a vertical tangent at the endpoints
show that the addition of the type dg/dx to the integrand function leaves the euler equation in the same form
Show that p(x)=lim(€n) where x=(€n) belongs to l(infinity) defines a sublinear functional on l(infinity)
if x0 in.norm space x is. such that |f(x0)|<= c for all.f€x' of norm 1 show that ||x0||=<c
show that absolute value of. a linear functional has properties of sublinear functional
Does N satisfy the Archimedean property ? Justify your answer
Find all the asymptototes of the curve x^3 + y^3 = 3axy
Check whether the function is periodic or not f(x)= cosec2x + cotx .If it is periodic then find it's period
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